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This article investigates the dynamics of optical solitons in a magneto-optic waveguide with the nonlinear perturbed Schrödinger equation. The model incorporates two generalized nonlocal laws, a Kudryashov's sextic-power law nonlinear structure, and high dispersion up to the sixth-order dispersion. The proposed innovative model ensures that all the obtained solutions are original and have not been reported elsewhere. The impetus for this work is the recognition of the crucial significance of studying nonlinear magneto-optical interactions in optical communication systems. The nonlinear Schrödinger equation and its derivatives play crucial roles in various scientific areas, particularly in the field of nonlinear optics and optical fibers. In order to investigate the new structure of our model, we utilize the Z ′ Z -expansion technique and the enhanced Kudrtashov's method. The solitons obtained are of several types, including bright, singular, and combinations thereof as well as kink-type solution. The strategies utilized are efficacious and distinctive tools in their methodologies and results. To further elucidate the dynamics of the acquired solitons, we offer a discussion section where we present plots of specific solitons. [ABSTRACT FROM AUTHOR]

A method is presented for the construction of W shaped-W shaped solitons and W-shaped soliton combined with other types of solitons to coupled nonlinear partial differential equations (NLPDEs). This method is applied to investigate the propagation of new progressive solitons in magneto-optical waveguides that carry the quadratic-cubic nonlinearity described by a coupled system of nonlinear Schr o ¨ dinger equations. These waveguides have a great advantage since they control solitons' clutter effects and thus assure their smooth propagation across intercontinental distances. Many approaches to investigating the exact solitons and other solutions to nonlinear models are often very powerful and very efficient to deal with single NLPDEs, however they do not always have the same success when applied to coupled NLPDEs. This difficulty is due to the existence of interaction terms in the coupled equations. For this reason, it is not always an easy task to derive exact solutions to these coupled equations. To overcome this difficulty, several authors have attempted to solve coupled equations by making the assumption that the solution in one line is proportional to the solution in another line, leading to an excessive imposition of constraints. This leads to the reduction of coupled equations to a single one. By doing so, they denature the physical phenomena described by the original coupled NLPDEs. We propose here a method that gives a better perspective in handling the analytical investigation of coupled NLPDEs. The novelty lies on the fact that it not only allows the propagation of different types of solutions in two lines to be conducted in just one move, but it also retrieves the propagation of same types of solutions in the two lines. For this latter case, the solutions come naturally with less constraints.The criteria for these solutions to exist are also exhibited in the form of parameter constraints. [ABSTRACT FROM AUTHOR]

In this paper, the traveling wave solutions of the model of magneto-optic waveguide with anti-cubic nonlinearity are obtained by using the complete discrimination system for polynomial method, including singular solutions, solitary wave solutions,and double periodic solutions. And under specific parameter conditions, three types of optical wave patterns are obtained to visualize the model and demonstrate their accurate physical behavior. Then the dynamic properties of Schrödinger equation in magneto-optic waveguide with anti-cubic nonlinearity are analyzed, the existence of periodic and solitary solutions is proved based on the bifurcation method. Also the Hamiltonian properties and the classification of its equilibrium points are obtained. In final, we analyze the chaotic behavior of the model under some external perturbations.

The current paper focuses on the retrieval of solitons in magneto-optic waveguides for the concatenation model having Kerr law of nonlinear refractive index. The simplest equation approach as well as the extended simplest equation method collectively reveal a full spectrum of soliton solutions to the model. The parameter constraints guarantee the existence of such solitons. [ABSTRACT FROM AUTHOR]

In this paper, the traveling wave solutions of the model of magneto-optic waveguide with anti-cubic nonlinearity are obtained by using the complete discrimination system for polynomial method, including singular solutions, solitary wave solutions,and double periodic solutions. And under specific parameter conditions, three types of optical wave patterns are obtained to visualize the model and demonstrate their accurate physical behavior. Then the dynamic properties of Schrödinger equation in magneto-optic waveguide with anti-cubic nonlinearity are analyzed, the existence of periodic and solitary solutions is proved based on the bifurcation method. Also the Hamiltonian properties and the classification of its equilibrium points are obtained. In final, we analyze the chaotic behavior of the model under some external perturbations. • This paper use the traveling wave transformation to convert the equation into a dynamic system and obtain its Hamiltonian properties. • Based on the bifurcation method, the existence of cycles and solitary solutions is proved. • The equation is analyzed using the complete discrimination system for polynomial method, and all its traveling wave solutions are obtained. • The external perturbation terms, in order to analyze the chaotic behavior of this equation. [ABSTRACT FROM AUTHOR]

This paper obtains the exact solution for solitons propagating through magneto-optic waveguides. There are three forms of nonlinear media that are considered. They are Kerr law, power law and log-law nonlinearity. The ansatz approach retrieves bright, dark as well as singular soliton solutions. There are several constraint conditions that needs to be in place for the solitons and Gaussons to exist. [ABSTRACT FROM AUTHOR]

This is a work on recovering soliton solutions in magneto-optic waveguides that maintains Kudryashov's generalized form of nonlinear refractive index. The unified auxiliary equation approach retrieves solutions in terms of Jacobi's elliptic functions. Subsequently, the limiting approach, when modulus of ellipticity approaches zero or unity, solitons and other solutions are identified. The paper concludes with an exhibit of conservation laws to the model. [ABSTRACT FROM AUTHOR]

To evaluate nonreciprocal phase characteristics of a magneto-optic channel waveguide, the formulation of a finite-element method based on a scalar wave approximation is discussed here for the first time. This problem is ascribed to the problem of solving a nonlinear eigenvalue equation. However, a simple iterative method is proposed here for solving the nonlinear eigenvalue equation. The validity and usefulness of the present method are demonstrated in analyzing magneto-optic rib wave- guides and magneto-optic ridge waveguides. A discussion to increase a nonreciprocal phase shift in those wave- guides also is given. [ABSTRACT FROM AUTHOR]

This paper secures bright, singular and combo optical solitons in magneto-optic waveguides with quadratic-cubic nonlinearity. Subsequently, the multiplier approach reveals three conserved quantities that are computed with the aid of the bright soliton solutions recovered from traveling wave hypothesis. [ABSTRACT FROM AUTHOR]

This paper secures bright and singular perturbed optical solitons in magneto-optic waveguides, having parabolic form of nonlinearity, with traveling wave hypothesis. The conservation laws are subsequently obtained by the multiplier approach and the three conserved quantities are finally listed. [ABSTRACT FROM AUTHOR]

• Bright, dark and singular solitons in magneto–optic waveguides are revealed. • Quadratic–cubic form of nonlinear refractive index is considered. • Unified Riccati equation expansion scheme and extended auxiliary equation method are implemented. This paper implements unified Riccati equation expansion scheme as well as extended auxiliary equation method to obtain bright, dark and singular solitons in magneto–optic waveguides. The quadratic–cubic form of nonlinear refractive index is the focus of the paper. These solitons emerge after a limiting value when the modulus of ellipticity approaches unity. [ABSTRACT FROM AUTHOR]