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345 results on '"Belic, A."'

13. Conservation laws for pure-cubic optical solitons with complex Ginzburg–Landau equation having several refractive index structures

Author

Anjan Biswas, Abdul H. Kara, Yunzhou Sun, Qin Zhou, Yakup Yıldırım, Hashim M. Alshehri, and Milivoj R. Belic

Subjects
Solitons, Conservation laws, Ginzburg–Landau equation, Physics, QC1-999
Abstract

This paper derives the conserved densities for the perturbed complex Ginzburg–Landau model which is addressed with a range of nonlinear forms. The densities are derived with the implementation of Lie symmetry analysis while the conserved quantities are obtained from the soliton solutions to the model. For two such nonlinear forms the Hamiltonian cease to exist since the corresponding integrals are rendered divergent.

Published
2021
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14. Highly dispersive optical soliton perturbation with Kudryashov’s sextic-power law nonlinear refractive index by semi-inverse variation

Author

Anjan Biswas, Mehmet Ekici, Anelia Dakova, Salam Khan, Seithuti P. Moshokoa, Hashim M. Alshehri, and Milivoj R. Belic

Subjects
Kudryashov, Solitons, Semi-inverse, Cardano, Perturbation, Physics, QC1-999
Abstract

A single bright highly dispersive optical soliton solution is recovered from semi-inverse variational principle. The model contains six power law nonlinear terms that constitute self-phase modulation effect which was proposed by Kudryashov. The amplitude–width relation of the soliton was finally recovered by Cardano’s approach with appropriate and necessary constraints that are presented.

Published
2021
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15. Cubic–quartic optical soliton perturbation with Fokas–Lenells equation by sine–Gordon equation approach

Author

Yakup Yıldırım, Anjan Biswas, Anelia Dakova, Salam Khan, Seithuti P. Moshokoa, Abdullah Khamis Alzahrani, and Milivoj R. Belic

Subjects
Solitons, Cubic–quartic, Perturbation, Fokas–Lenells, Physics, QC1-999
Abstract

This paper recovers cubic–quartic optical solitons for perturbed Fokas–Lenells equation in polarization-preserving fibers and birefringent fibers. The perturbation terms appear with maximum permissible intensity. Singular and dark solitons, together with a few combo solitons, emerge from the sine–Gordon equation integration scheme.

Published
2021
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17. Optical solitons with differential group delay for complex Ginzburg–Landau equation

Author

Yakup Yıldırım, Anjan Biswas, Anwar Ja’afar Mohamad Jawad, Mehmet Ekici, Qin Zhou, Abdullah Kamis Alzahrani, and Milivoj R. Belic

Subjects
Solitons, Integrability, Birefringence, Physics, QC1-999
Abstract

This paper addresses optical solitons in birefringent fibers that is modeled by complex Ginzburg–Landau equation with Kerr law nonlinearity. Three forms of integration architecture retrieves soliton and other solutions to the model. The solitons are classified and their existence criteria are also presented.

Published
2020
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19. Embedded solitons with Χ(2) nonliner susceptibility.

Author

Yıldırım, Y., Biswas, A., Ekici, M., Khan, S., Triki, H., Moraru, L., Alzahrani, A. K., and Belic, M. R.

Subjects
SOLITONS, RICCATI equation, SINE-Gordon equation
Abstract

This paper recovers optical soliton solutions with Χ(2)-nonlinear susceptibility. Bright, dark, singular, bright-dark combo solitons are recovered. A variety of algorithms are implemented. These include the Riccati equation approach, exp-function expansion method, modified simple equation algorithm, sine-Gordon equation scheme, F-expansion approach, trial function method, and functional variable algorithm. [ABSTRACT FROM AUTHOR]

Published
2023
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25. Conservation laws for pure-cubic optical solitons with complex Ginzburg–Landau equation having several refractive index structures

Author

Yun-Zhou Sun, Yakup Yıldırım, Qin Zhou, Milivoj R. Belic, Abdul H. Kara, Anjan Biswas, and Hashim M. Alshehri

Subjects
Physics, Conservation law, QC1-999, General Physics and Astronomy, Conserved quantity, Solitons, Symmetry (physics), symbols.namesake, Nonlinear system, Range (mathematics), symbols, Soliton, Hamiltonian (quantum mechanics), Refractive index, Mathematical physics, Conservation laws, Ginzburg–Landau equation
Abstract

This paper derives the conserved densities for the perturbed complex Ginzburg–Landau model which is addressed with a range of nonlinear forms. The densities are derived with the implementation of Lie symmetry analysis while the conserved quantities are obtained from the soliton solutions to the model. For two such nonlinear forms the Hamiltonian cease to exist since the corresponding integrals are rendered divergent.

Published
2021

26. Optical soliton molecules in birefringent fibers having weak non-local nonlinearity and four-wave mixing with a couple of strategic integration architectures

Author

Yakup Yıldırım, Seithuti P. Moshokoa, Milivoj R. Belic, Salam Khan, Anjan Biswas, Qin Zhou, Samuel O. Adesanya, Emrullah Yaşar, Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik/Uygulamalı Matematik Bölümü., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Strategic integration, Optical soliton, Equation Method, Physics::Optics, Optical signal processing, Phase matching, Astrophysics::Cosmology and Extragalactic Astrophysics, 02 engineering and technology, Solitons, 01 natural sciences, Molecular physics, Phase matching conditions, 010309 optics, Four-wave mixing, Non-local nonlinearity, 0103 physical sciences, Molecule, Electrical and Electronic Engineering, Nonlocal, Singular soliton solutions, Nonlinear Sciences::Pattern Formation and Solitons, Mixing (physics), Physics, Birefringence, Optics, 021001 nanoscience & nanotechnology, Non local, Four wave mixing, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials, Nonlinear system, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Nematic Liquid Crystals, Soliton, 0210 nano-technology, Birefringent fibers
Abstract

This paper retrieves optical solitons in birefringent fibers having non-local nonlinearity in presence of four-wave mixing. Phase-matching conditions have been implemented to display these solitons. Bright, dark and singular soliton solutions are revealed. Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation --- 92052 IRF1202210126 National Research Foundation of Korea --- NPRP 8-028-1-001 Qatar National Research Fund (QNRF)

Published
2019
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27. Highly dispersive optical soliton perturbation with Kudryashov’s sextic–power law nonlinear refractive index by semi–inverse variation

Author

Hashim M. Alshehri, Anjan Biswas, Mehmet Ekici, Milivoj R. Belic, A. Dakova, Salam Khan, and Seithuti P. Moshokoa

Subjects
Physics, Kudryashov, Solitons, Semi-inverse, Cardano, Perturbation, QC1-999, Cardano, Mathematical analysis, General Physics and Astronomy, Inverse, Perturbation (astronomy), Nonlinear refractive index, Kudryashov, Solitons, Power law, Perturbation, Nonlinear system, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Variational principle, Semi-inverse, Soliton, Variation (astronomy)
Abstract

A single bright highly dispersive optical soliton solution is recovered from semi-inverse variational principle. The model contains six power law nonlinear terms that constitute self-phase modulation effect which was proposed by Kudryashov. The amplitude–width relation of the soliton was finally recovered by Cardano’s approach with appropriate and necessary constraints that are presented.

Published
2021

28. Sub pico-second pulses in mono-mode optical fibers with Kaup–Newell equation by a couple of integration schemes

Author

Emrullah Yaşar, Seithuti P. Moshokoa, Yakup Yıldırım, Qin Zhou, Milivoj R. Belic, Anjan Biswas, Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Wave-guides, Optical fiber, Constraint relations, Simple equation, Geometry, 02 engineering and technology, Solitons, 01 natural sciences, law.invention, 010309 optics, law, 0103 physical sciences, Optical fibers, Darkness, Media Law, Periodic Solution, Electrical and Electronic Engineering, Soliton dynamics, Nonlinear Sciences::Pattern Formation and Solitons, Pico-second pulse, Physics, Mathematical analysis, Mode (statistics), Optics, Self-phase modulation, Integration scheme, 021001 nanoscience & nanotechnology, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials, Constraint (information theory), Modified simple equation method, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Picosecond, Soliton, Trial equation method, 0210 nano-technology
Abstract

This paper examines soliton dynamics of sub pico-second pulses modeled by Kaup–Newell equation. The modified simple equation scheme and trial equation approach retrieves dark, bright as well as singular solitons to the model. The constraint relations guarantee the existence of such solitons.

Published
2018
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29. Optical solitons with differential group delay for coupled Fokas–Lenells equation using two integration schemes

Author

Mohammad F. Mahmood, Seithuti P. Moshokoa, Yakup Yıldırım, Qin Zhou, Milivoj R. Belic, Emrullah Yaşar, Anjan Biswas, Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
System, Optical fiber, Optical soliton, Simple equation, 02 engineering and technology, Trial equation methods, Solitons, 01 natural sciences, law.invention, 010309 optics, Differential group delay, law, 0103 physical sciences, Optical fibers, Electrical and Electronic Engineering, Singular soliton solutions, Physics, Mathematical analysis, Optics, Group delay, Integration scheme, 021001 nanoscience & nanotechnology, Optical Solitons, Nonlinear Schrödinger Equation, Lax Pair, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials, Modified simple equation method, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Scheme (mathematics), Soliton, Trial equation method, 0210 nano-technology
Abstract

This paper studies differential group delay in optical fibers with coupled Fokas-Lenells equation. Two integration schemes are adopted. They are trial equation method and modified simple equation scheme. Bright, dark and singular soliton solutions are retrieved together with their respective existence criteria that are also presented. Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation (92052 IRF1202210126) National Research Foundation of Korea Qatar National Research Fund (QNRF) (NPRP 8-028-1-001)

Published
2018
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30. Dispersive optical solitons with Schrödinger–Hirota model by trial equation method

Author

Emrullah Yaşar, Qin Zhou, Yakup Yıldırım, Ali Saleh Alshomrani, Anjan Biswas, Milivoj R. Belic, Seithuti P. Moshokoa, Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Optical soliton, Dispersive solitons, 02 engineering and technology, Solitons, 01 natural sciences, Power law, 010309 optics, symbols.namesake, 0103 physical sciences, Darkness, Media Law, Periodic Solution, Electrical and Electronic Engineering, Nonlinear Sciences::Pattern Formation and Solitons, Mathematical physics, Physics, Power-law, Optics, 021001 nanoscience & nanotechnology, Control nonlinearities, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials, Nonlinear system, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Hirota equation, Periodic solution, symbols, Soliton, Trial equation method, 0210 nano-technology, Schrödinger's cat
Abstract

This paper obtains bright, dark and singular dispersive optical soliton solutions to Schrodinger-Hirota equation by the aid of trial equation method. Both Kerr and power laws of nonlinearity are studied. Singular periodic solutions are also obtained as a byproduct of this scheme. Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation (92052 IRF1202210126) National Research Foundation of Korea Qatar National Research Fund (QNRF) (NPRP 8-028-1-001)

Published
2018
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31. Optical solitons for Lakshmanan–Porsezian–Daniel model by modified simple equation method

Author

Anjan Biswas, Seithuti P. Moshokoa, Emrullah Yaşar, Milivoj R. Belic, Qin Zhou, Yakup Yıldırım, Uludağ Üniversitesi/Fen Bilimleri Enstitüsü/Matematik Anabilim Dalı., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Coefficients, Optical soliton, Simple equation, 02 engineering and technology, Solitons, 01 natural sciences, 010309 optics, Cubic laws, Soliton solutions, Constraint conditions, 0103 physical sciences, Kerr law, Darkness, Media Law, Periodic Solution, Electrical and Electronic Engineering, Singular soliton solutions, Nonlinear Sciences::Pattern Formation and Solitons, Physics, Optical properties, Parabolic law, Mathematical analysis, Optics, 021001 nanoscience & nanotechnology, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials, Constraint (information theory), Modified simple equation method, Scheme (mathematics), Soliton, 0210 nano-technology
Abstract

The soliton solutions are extracted from the Lakshmanan-Porsezian-Daniel model by the aid of modified simple equation method. There are three forms of fibers that are studied and they represent Kerr law, parabolic law and anti-cubic law. The implementation of the scheme yields dark and singular soliton solutions to the model. The constraint conditions hold these solitons in place. Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation (92052 IRF1202210126) National Research Foundation of Korea Qatar National Research Fund (QNRF) (NPRP 8-028-1-001)

Published
2018
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32. Optical soliton perturbation with Gerdjikov–Ivanov equation by modified simple equation method

Author

Ali Saleh Alshomrani, Seithuti P. Moshokoa, Houria Triki, Yakup Yıldırım, Milivoj R. Belic, Malik Zaka Ullah, Emrullah Yaşar, Qin Zhou, Anjan Biswas, Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Optical fiber, Perturbation techniques, Optical soliton, Simple equation, Physics::Optics, Perturbation (astronomy), 02 engineering and technology, Solitons, 01 natural sciences, law.invention, 010309 optics, Solvability conditions, law, 0103 physical sciences, Optical fibers, Darkness, Media Law, Periodic Solution, Pulse dynamics, Electrical and Electronic Engineering, Physics, Optics, 021001 nanoscience & nanotechnology, Atomic and Molecular Physics, and Optics, Perturbation, Electronic, Optical and Magnetic Materials, Modified simple equation method, Classical mechanics, Integrable systems, 0210 nano-technology
Abstract

The modified simple equation scheme is employed to secure dark and singular optical soliton solution to the perturbed Gerdjikov-Ivanov equation that models pulse dynamics in optical fibers and PCF. The solvability conditions for this algorithm is also presented. National Science Foundation for Young Scientists of Wuhan Donghu University (2017dhzk001) Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation (92052 IRF1202210126) National Research Foundation of Korea Qatar National Research Fund (QNRF) (NPRP 8-028-1-001)

Published
2018
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33. Optical soliton perturbation with full nonlinearity for Gerdjikov–Ivanov equation by trial equation method

Author

Yakup Yıldırım, Emrullah Yaşar, Houria Triki, Seithuti P. Moshokoa, Malik Zaka Ullah, Qin Zhou, Ali Saleh Alshomrani, Anjan Biswas, Milivoj R. Belic, Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Physics, Optical soliton, Integrable Couplings, Trace Identity, Spectral Problem, Perturbation (astronomy), Optics, 02 engineering and technology, Integration scheme, 021001 nanoscience & nanotechnology, Solitons, 01 natural sciences, Control nonlinearities, Atomic and Molecular Physics, and Optics, Perturbation, Electronic, Optical and Magnetic Materials, 010309 optics, Nonlinear system, Periodic solution, 0103 physical sciences, Integrable systems, Trial equation method, Electrical and Electronic Engineering, Singular soliton solutions, 0210 nano-technology, Nonlinear Sciences::Pattern Formation and Solitons, Mathematical physics
Abstract

This paper obtains optical soliton solution to perturbed Gerdjikov-Ivanov equation by trial equation approach. Bright, dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also emerge of this integration scheme. National Science Foundation for Young Scientists of Wuhan Donghu University (2017dhzk001) Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation (92052 IRF1202210126) National Research Foundation of Korea Qatar National Research Fund (QNRF) (NPRP 8-028-1-001)

Published
2018
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34. Optical solitons and conservation law of Kundu–Eckhaus equation

Author

Seithuti P. Moshokoa, Anjan Biswas, Houria Triki, Aly R. Seadawy, Malik Zaka Ullah, Qin Zhou, Milivoj R. Belic, Mohammad Mirzazadeh, Yakup Yıldırım, Emrullah Yaşar, Uludağ Üniversitesi/Fen Bilimleri Enstitüsü/Matematik Anabilim Dalı., Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Optical soliton, Bright solitons, 02 engineering and technology, Integrability, Conservation law, Solitons, 01 natural sciences, 010309 optics, Soliton solutions, Quantum mechanics, 0103 physical sciences, Kudryashov method, Conserved quantity, Electrical and Electronic Engineering, Nonlinear Sciences::Pattern Formation and Solitons, Mathematical physics, Physics, Optical properties, Bernoulli, Optics, Exact Solution, Optical Solitons, (G′/G)-expansion Method, 021001 nanoscience & nanotechnology, Dark, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials, Fibers, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Scheme (mathematics), Soliton, 0210 nano-technology
Abstract

This paper obtains optical soliton solutions to the Kundu Eckhaus equation with general coefficients. The Riccati Bernoulli's sub-ODE method as well as Kudryashov's scheme are employed to obtain soliton solutions to the model. This generalized earlier reported result of the model with specific coefficients. Subsequently, the multiplier approach was utilized to secure a conserved quantity with the bright soliton solution that was reported earlier. Young Foundation of Wuhan Donghu University (2017DHKZ001) Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation (92052 IRF1202210126) Qatar National Research Fund (QNRF) (NPRP 8-028-1-001)

Published
2018
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35. Optical solitons in fiber Bragg gratings with quadratic-cubic law of nonlinear refractive index and cubic-quartic dispersive reflectivity.

Author

Zayed, Elsayed M. E., Alngar, Mohamed E. M., Biswas, Anjan, Ekici, Mehmet, Khan, Salam, Alzahrani, Abdullah K., and Belic, Milivoj R.

Subjects
FIBER Bragg gratings, REFRACTIVE index, OPTICAL solitons, OPTICAL fibers, RICCATI equation, BRAGG gratings, SOLITONS
Abstract

This paper recovers cubic-quartic perturbed solitons in fiber Bragg gratings with quadratic-cubic law nonlinear refractive index. The unified Riccati equation expansion method and the modified Kudryashov’s approach make this retrieval of soliton solutions possible. The parameter constraints, for the existence of such solitons, are also presented. [ABSTRACT FROM AUTHOR]

Published
2022
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36. Dynamical system of optical soliton parameters for anti-cubic and generalized anti-cubic nonlinearities with super-Gaussian and super-sech pulses.

Author

AYELA, AMOUR MARC, EDAH, GASTON, BISWAS, ANJAN, QIN ZHOU, YILDIRIM, YAKUP, KHAN, SALAM, ALZAHRANI, ABDULLAH K., and BELIC, MILIVOJ R.

Subjects
DYNAMICAL systems, OPTICAL solitons, LINEAR momentum, VARIATIONAL principles, OPTICAL fibers, SOLITONS
Abstract

The parameter dynamics of solitons, propagating through optical fibers, is emerged from the usage of variational principle. The anti-cubic nonlinearity and its generalized version are studied. This study reveals that the center position does not affect the dynamics of different parameters and only soliton power and linear momentum are conserved quantities. [ABSTRACT FROM AUTHOR]

Published
2022
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37. Cubic-quartic optical soliton perturbation with Fokas-Lenells equation by semi-inverse variation.

Author

Biswas, A., Dakova, A., Khan, S., Ekici, M., Moraru, L., and Belic, M. R.

Subjects
PERTURBATION theory, OPTICAL solitons, VARIATIONAL principles, SOLITONS
Abstract

This paper recovers cubic-quartic bright optical solitons with perturbed Fokas-Lenells equation. The Hamiltonian perturbation terms appear with maximal permissible intensity. The semi-inverse variational principle is employed to retrieve such solitons. [ABSTRACT FROM AUTHOR]

Published
2021
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38. Cubic–quartic optical soliton perturbation and conservation laws with Lakshmanan–Porsezian–Daniel model: Undetermined coefficients.

Author

Vega-Guzman, Jose, Biswas, Anjan, Kara, Abdul Hamid, Mahmood, M. F., Ekici, Mehmet, Alshehri, Hashim M., and Belic, Milivoj R.

Subjects
CONSERVATION laws (Physics), SOLITONS, OPTICAL solitons, FIBERS
Abstract

This work recovers cubic–quartic soliton solutions to the Lakshmanan–Porsezian–Daniel model by the method of undetermined coefficients. Both polarization-preserving fibers and birefringent fibers are studied. The conservation laws for polarization-preserving fibers are also retrieved and enumerated. The existence criteria for the displayed solitons are also presented. [ABSTRACT FROM AUTHOR]

Published
2021
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39. Cubic–quartic polarized optical solitons and conservation laws for perturbed Fokas–Lenells model.

Author

Zayed, Elsayed M. E., Alngar, Mohamed E. M., El-Horbaty, Mahmoud M., Biswas, Anjan, Kara, Abdul H., Yıldırım, Yakup, Khan, Salam, Alzahrani, Abdullah Khamis, and Belic, Milivoj R.

Subjects
CONSERVATION laws (Physics), OPTICAL solitons, CONSERVED quantity, SOLITONS
Abstract

This paper studies polarized cubic–quartic solitons that are modeled by Fokas–Lenells equation in birefringent fibers. Two integration schemes recovered a spectrum of soliton solutions to the model. Subsequently, the bright solitons compute the corresponding conserved quantities from the respective densities that are recovered by the multiplier approach. [ABSTRACT FROM AUTHOR]

Published
2021
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40. Solitions in magneto–optic waveguides with anti–cubic nonlinearity

Author

Mohamed E.M. Alngar, Abdullah Kamis Alzahrani, Reham M.A. Shohib, Milivoj R. Belic, Elsayed M.E. Zayed, Anjan Biswas, and Mehmet Ekici

Subjects
Magneto–optic, Physics, Cubic nonlinearity, Spectrum (functional analysis), Mathematical analysis, Elliptic function, Physics::Optics, Modulus, Nonlinear refractive index, 02 engineering and technology, Limiting, anti–cubic nonlinearity, 021001 nanoscience & nanotechnology, Solitons, 01 natural sciences, Article, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials, 010309 optics, 0103 physical sciences, Soliton, Electrical and Electronic Engineering, 0210 nano-technology, Nonlinear Sciences::Pattern Formation and Solitons, Magneto
Abstract

Optical soliton solutions are recovered for magneto–optic waveguides that maintains anti–cubic form of nonlinear refractive index. The analytical scheme is Jacobi's elliptic function approach. Once the solutions to the governing model are obtained in terms of Jacobi's elliptic functions, the limiting value to it's modulus of ellipticity reveals the complete spectrum of soliton solutions.

Published
2020
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41. Optical solitons in birefringent fibers with weak non-local nonlinearity using two forms of integration architecture

Author

Yakup Yıldırım, Qin Zhou, Anjan Biswas, Mohanad Alfiras, Milivoj R. Belic, Emrullah Yaşar, Seithuti P. Moshokoa, Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Simple equation, MathematicsofComputing_NUMERICALANALYSIS, 02 engineering and technology, 01 natural sciences, Solitons, 010309 optics, Equation medhot, Trial equation, 0103 physical sciences, Electrical and Electronic Engineering, Nonlinear Sciences::Pattern Formation and Solitons, Physics, Birefringence, Integration architecture, Optics, 021001 nanoscience & nanotechnology, Non local, Dark, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials, Nonlinear system, Classical mechanics, Nematic Liquid Crystals, Nonlocal, Soliton, 0210 nano-technology, Modified simple equation
Abstract

This paper implements two efficient integration algorithms to retrieve soliton solutions that appear with weak nonlocal nonlinearity. These are trial equation method and modified simple equation scheme. Bright, dark and singular soliton solutions are recovered and their existence criteria are also presented. Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation (92052 IRF1202210126) National Research Foundation of Korea Qatar National Research Fund (QNRF) (NPRP 8-028-1-001)

Published
2019

42. Optical soliton solutions to Fokas-lenells equation using some different methods

Author

Qin Zhou, Anjan Biswas, Yakup Yıldırım, Emrullah Yaşar, Seithuti P. Moshokoa, Milivoj R. Belic, Bursa Uludağ Üniversitesi/Fen Bilimleri Enstitüsü/Matematik Anabilim Dalı., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Optical fiber, Simple equation, Context (language use), 060.5530, 02 engineering and technology, 01 natural sciences, Solitons, Optical soliton solutions, law.invention, 010309 optics, 190.4370, law, 0103 physical sciences, Fokas-Lenells equation, Optical fibers, Electrical and Electronic Engineering, Nonlinear Sciences::Pattern Formation and Solitons, Physics, Optics, Exact Solution, Optical Solitons, (G′/G)-expansion Method, 021001 nanoscience & nanotechnology, Atomic and Molecular Physics, and Optics, 060.4510, Electronic, Optical and Magnetic Materials, 060.2310, Modified simple equation method, 190.3270, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Classical mechanics, Soliton, Trial equation method, 0210 nano-technology
Abstract

Dark and bright with singular solitons shall be yielded to Fokas–Lenells equation which describes soliton dynamics in optical fibers. The two integration schemes that are applied in this context are the modified simple equation method and the trial equation method. Additional solutions, besides, optical solitons, are recovered.

Published
2018

43. Optical soliton perturbation for Radhakrishnan–Kundu–Lakshmanan equation with a couple of integration schemes

Author

Anjan Biswas, Mohammad F. Mahmood, Emrullah Yaşar, Qin Zhou, Ali Saleh Alshomrani, Yakup Yıldırım, Milivoj R. Belic, Seithuti P. Moshokoa, Uludağ Üniversitesi/Fen Bilimleri Enstitüsü/Matematik Anabilim Dalı., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Optical soliton, Simple equation, Perturbation (astronomy), 02 engineering and technology, Trial equation methods, 01 natural sciences, Power law, Solitons, Trial function scheme, 010309 optics, Non-linear fiber, 0103 physical sciences, Darkness, Media Law, Periodic Solution, Electrical and Electronic Engineering, Singular soliton solutions, Nonlinear Sciences::Pattern Formation and Solitons, Mathematical physics, Physics, Optical properties, Power-law, Optics, 021001 nanoscience & nanotechnology, Nonliear directional-couplers, Integration scheme, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials, Nonlinear system, Modified simple equation method, Periodic solution, Trial equation method, 0210 nano-technology
Abstract

This paper obtains optical soliton solutions to the perturbed Radhakrishnan-Kundu-Lakshmanan equation by trial equation method and modified simple equation algorithm. There are two types of nonlinear fibers studied in this paper. They are Kerr law and power law. Bright, dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration schemes. Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation (92052 IRF1202210126) National Research Foundation of Korea Qatar National Research Fund (QNRF) (NPRP 8-028-1-001)

Published
2018

44. Embedded solitons with X(2) and X(3) nonlinear susceptibilities.

Author

Yildirim, Y., Biswas, A., Khan, S., and Belic, M. R.

Subjects
NONLINEAR Schrodinger equation, DISPERSION (Chemistry), SOLITONS
Abstract

Studied in this work are embedded solitons with quadratic nonlinearity that includes the effect of spatio-temporal dispersion. Two integration schemes yield bright, dark, singular and combo singular soliton solutions from the continuous regime. The existence criteria for these solitons are also included. [ABSTRACT FROM AUTHOR]

Published
2021
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45. Optical soliton perturbation with Kudryashov's law of refractive index by modified sub-ODE approach.

Author

Zayed, Elsayed M. E., Alngar, Mohamed E. M., Shohib, Reham M. A., Khan, Salam, Biswas, Anjan, Dakova, Anelia, Alzahrani, Abdullah Khamis, and Belic, Milivoj R.

Subjects
REFRACTIVE index, SELF-phase modulation, ELLIPTIC functions, OPTICAL solitons, SOLITONS
Abstract

This paper implements the sub-ODE method and a wide spectrum of solitons are recovered for Kudryashov's law of refractive index. The self-phase modulation comprises of four nonlinear components of refractive index. The perturbation terms are all of Hamiltonian type and are considered with maximum intensity. The solutions are written in terms of Weierstrass' elliptic functions and Jacobi's elliptic function. With the modulus of ellipticity approaching zero or unity, soliton solutions emerge. [ABSTRACT FROM AUTHOR]

Published
2021
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46. Optical soliton perturbation with resonant nonlinear Schrödinger's equation having full nonlinearity by modified simple equation method

Author

Emrullah Yaşar, Seithuti P. Moshokoa, Qin Zhou, Milivoj R. Belic, Yakup Yıldırım, Anjan Biswas, Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Nonlinear optics, Optical soliton, Simple equation, Perturbation (astronomy), 02 engineering and technology, 01 natural sciences, Solitons, Full nonlinearity, 010309 optics, symbols.namesake, Cubic laws, Power-law nonlinearity, Time-dependent coefficients, Soliton solutions, Constraint conditions, 0103 physical sciences, Kerr law, Darkness, Media Law, Periodic Solution, Electrical and Electronic Engineering, Nonlinear Sciences::Pattern Formation and Solitons, Physics, Nonlinear equation, Optics, 021001 nanoscience & nanotechnology, Atomic and Molecular Physics, and Optics, Control nonlinearities, Electronic, Optical and Magnetic Materials, Perturbation, Nonlinear system, Classical mechanics, symbols, Non-Kerr law, 0210 nano-technology, Schrödinger's cat
Abstract

This paper retrieves soliton solutions to the perturbed resonant nonlinear Schrodinger's equation with time-dependent coefficients using the modified simple equation method. The four types of exotic non-Kerr laws studied in this paper are quadratic-cubic law, anti cubic law, cubic-quintic-septic law and triple-power law. These soliton solutions appear with constraint conditions that guarantee their existence. Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation (92052 IRF1202210126) National Research Foundation of Korea Qatar National Research Fund (QNRF) (NPRP 8-028-1-001)

Published
2018

47. Optical soliton perturbation with complex Ginzburg–Landau equation using trial solution approach

Author

Seithuti P. Moshokoa, Malik Zaka Ullah, Yakup Yıldırım, Houria Triki, Emrullah Yaşar, Milivoj R. Belic, Qin Zhou, Ali Saleh Alshomrani, Anjan Biswas, Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Physics, Ginzburg landau equation, Perturbation (astronomy), Optics, 02 engineering and technology, 021001 nanoscience & nanotechnology, 01 natural sciences, Solitons, Full nonlinearity, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials, Perturbation, 010309 optics, Nonlinear system, Law-nonlinearity, 0103 physical sciences, Integration algorithm, Soliton, Non-Kerr law, Darkness, Media Law, Periodic Solution, Electrical and Electronic Engineering, Trial equation method, 0210 nano-technology, Nonlinear Sciences::Pattern Formation and Solitons, Mathematical physics
Abstract

This paper retrieves optical soliton solution to the perturbed complex Ginzburg-Landau equation that is studied with nine different forms of nonlinearity. The trial solutions approach is the integration algorithm adopted in this paper. The perturbation terms appear with full nonlinearity to get a taste of generalized setting. Bright, dark and singular soliton solutions are obtained. The existence criteria of such solitons are also presented. Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation (92052 IRF1202210126) National Research Foundation of Korea Qatar National Research Fund (QNRF) (NPRP 8-028-1-001)

Published
2018

48. Optical solitons with differential group delay by trial equation method

Author

Anjan Biswas, Yakup Yıldırım, Milivoj R. Belic, Qin Zhou, Emrullah Yaşar, Seithuti P. Moshokoa, Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Constraint relations, Optical soliton, Physics::Optics, 02 engineering and technology, 01 natural sciences, Solitons, 010309 optics, Differential group delay, Soliton solutions, 0103 physical sciences, Kerr law, Darkness, Media Law, Periodic Solution, Electrical and Electronic Engineering, Nonlinear Sciences::Pattern Formation and Solitons, Physics, Parabolic law nonlinearity, Birefringence, Parabolic law, Mathematical analysis, Optics, Group delay, 021001 nanoscience & nanotechnology, Atomic and Molecular Physics, and Optics, Control nonlinearities, Electronic, Optical and Magnetic Materials, Constraint (information theory), Nonlinear system, Soliton, Trial equation method, 0210 nano-technology, Birefringent fibers
Abstract

This paper secures bright, dark and singualr soliton solutions in birefringent fibers. Both Kerr law and parabolic law nonlinearity are studied. The trial equation method successfully retrieves these solitons with constraint relations that assure their existence. Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation (92052 IRF1202210126) National Research Foundation of Korea Qatar National Research Fund (QNRF) (NPRP 8-028-1-001)

Published
2018

49. Optical soliton perturbation for complex Ginzburg–Landau equation with modified simple equation method

Author

Emrullah Yaşar, Houria Triki, Seithuti P. Moshokoa, Qin Zhou, Malik Zaka Ullah, Ali Saleh Alshomrani, Yakup Yıldırım, Anjan Biswas, Milivoj R. Belic, Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Yıldırım, Yakup, Yaşar, Emrullah, and AAG-9947-2021

Subjects
Perturbation techniques, Optical soliton, Simple equation, Perturbation (astronomy), 02 engineering and technology, 01 natural sciences, Solitons, Full nonlinearity, 010309 optics, Modified simple equation equation method, Constraint conditions, 0103 physical sciences, Darkness, Media Law, Periodic Solution, Electrical and Electronic Engineering, Landau equation, Mathematical physics, Physics, Power-law nonliearity, Ginzburg landau equation, Singular solutions, Optics, 021001 nanoscience & nanotechnology, Atomic and Molecular Physics, and Optics, Control nonlinearities, Electronic, Optical and Magnetic Materials, Perturbation, Nonlinear system, Soliton, 0210 nano-technology
Abstract

The modified simple equation method applied to perturbed complex Ginzburg-Landau equation gives dark and singular solutions to the model. The perturbation terms appear with full nonlinearity. There are eight nonlinear forms studied in this paper. These solitons appear with constraint conditions that gurantee its existence and these are also presented. Chutian Scholar Program of Hubei Government in China Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation (92052 IRF1202210126) National Research Foundation of Korea Qatar National Research Fund (QNRF) (NPRP 8-028-1-001)

Published
2017

50. Perturbed dark and singular optical solitons in polarization preserving fibers by modified simple equation method

Author

Yakup Yıldırım, Anjan Biswas, Houria Triki, Seithuti P. Moshokoa, Milivoj R. Belic, Emrullah Yaşar, Qin Zhou, Malik Zaka Ullah, Uludağ Üniversitesi/Fen-Edebiyet Fakültesi/Matematik Bölümü., Yaşar, Emrullah, Yıldırım, Yakup, and AAG-9947-2021

Subjects
Nonlinear optics, Perturbation techniques, Optical soliton, Simple equation, Perturbation (astronomy), 02 engineering and technology, 01 natural sciences, Solitons, 010309 optics, symbols.namesake, Cubic laws, Conservation-laws, Singular solution, Non-linear fiber, 0103 physical sciences, Kerr law media, General Materials Science, Spatiotemporal dispersion, Physics, condensed matter, Darkness, Media Law, Periodic Solution, Electrical and Electronic Engineering, Schrodingers equation, Singular soliton solutions, Nonlinear Sciences::Pattern Formation and Solitons, Physics, Nonlinear equations, 021001 nanoscience & nanotechnology, Condensed Matter Physics, Polarization (waves), Integration scheme, Anti-cubic nonlinearity, Perturbation, Nonlinear system, Modified simple equation method, Classical mechanics, Periodic solution, symbols, Soliton, 0210 nano-technology, Schrödinger's cat
Abstract

This paper obtains optical soliton solution to perturbed nonlinear Schrodinger's equation by modified simple equation method. There are four types of nonlinear fibers studied in this paper. They are Anti-cubic law, Quadratic-cubic law, Cubic-quintic-septic law and Triple-power law. Dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration scheme. National Natural Science Foundation of China (NSFC) - 2015CFC891 Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation - 92052 IRF1202210126 Qatar National Research Fund (QNRF) - NPRP 8-028-1-001 Tshwane University of Technology

Published
2017

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