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76 results on '"Yasar, Emrullah"'

5. Variational Operators, Symplectic Operators, and the Cohomology of Scalar Evolution Equations

Author

Fels, Mark E. and Yasar, Emrullah

Subjects
Mathematics - Differential Geometry, Mathematical Physics, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 37K10, 37K05, 58A20
Abstract

For a scalar evolution equation $u_t=K(t,x,u,u_x,\ldots, u_n), n\geq 2$ the cohomology spaces $H^{1,s}({\mathcal R}^\infty)$ vanishes for $s\geq 3$ while the space $H^{1,2}({\mathcal R}^\infty)$ is isomorphic to the space of variational operators. The cohomology space $H^{1,2}({\mathcal R}^\infty)$ is also shown to be isomorphic to the space of symplectic operators for $u_t=K$ for which the equation is Hamiltonian. Third order scalar evolution equations admitting a first order symplectic (or variational) operator are characterized. The symplectic nature of the potential form of a bi-Hamiltonian evolution equation is also presented., Comment: 42 pages

Published
2019

15. Prolific new M-fractional soliton behaviors to the Schrödinger type Ivancevic option pricing model by two efficient techniques.

Author

Ozkan, Yeşim Saglam and Yasar, Emrullah

Subjects
SCHRODINGER equation, OPTIONS (Finance), PROBABILITY theory, ECONOMIC models, BLACK-Scholes model
Abstract

The principal purpose of this research is to study the M-fractional nonlinear quantum-probability grounded Schrödinger kind Ivancevic option pricing model (IOPM). This well-known economic model is an alternative of the standard Black-Scholes pricing model which represents a controlled Brownian motion in an adaptive setting with relation to nonlinear Schrödinger equation. The exact solutions of the underlying equation have been derived through the well-organized extended modified auxiliary equation mapping and generalized exponential rational function methods. Different forms of optical wave structures including dark, bright, and singular solitons are derived. To the best of our knowledge, verified solutions using Maple are new. The results obtained will contribute to the enrichment of the existing literature of the model under consideration. Moreover, some sketches are plotted to show more about the dynamic behavior of this model. [ABSTRACT FROM AUTHOR]

Published
2024
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49. Lie group analysis, exact solutions and conservation laws of (3+1) dimensional a B-type KP equation.

Author

Yasar, Emrullah

Subjects
*LIE groups, *CONSERVATION laws (Mathematics), *EQUATIONS
Abstract

In this study, we considered the (3+1) dimensional a B-type Kademtsev-Petviashvili (KP) equation. Using the Lie group analysis, the symmetry reductions and exact analytic solutions were obtained. Traveling wave solutions were also deduced. Lastly, local conservation laws were constructed by using the multiplier and Ibragimov's nonlocal conservation method. [ABSTRACT FROM AUTHOR]

Published
2016
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50. Zaman Kesirli Beşinci Mertebeden Modifiye Edilmiş Sawada-Kotera Denkleminin Lie Simetri Analizi ve İlerleyen Dalga Çözümleri

Author

YASAR, Emrullah and YILDIRIM, Yakup

Subjects
Lie symmetry,Riemann-Liouville derivative,Time fractional modified Sawada-Kotera equation,Traveling wave solutions, Lie simetri,Riemann-Liouville türevi,Zaman kesirli modifiye edilmiş Sawada-Kotera denklemi,İlerleyen dalga çözümleri
Abstract

Bu makalede Riemann-Liouville türevine sahip beşinci mertebeden zaman kesirli modifiye edilmiş Sawada-Kotera denkleminin Lie grup analizi araştırılmıştır. Lie grup teorisinin denkleme uygulanmasıyla iki boyutlu Lie cebri elde edilmiştir. Aşikar olmayan Lie simetrisinin kullanılmasıyla denklemin Erdelyi-Kober kesirli türev operatörü cinsinden beşinci mertebeden kesirli adi diferensiyel denkleme dönüştürülebileceği gösterilmiştir. Bunun yanında alt-denklem metodu kullanılarak denklemin bazı tam ilerleyen dalga çözümlerine ulaşılmıştır, In this paper, we study Lie symmetry analysis of the time fractional fifth-order modified Sawada-Kotera equation FMSK with Riemann-Liouville derivative. Applying the adapted the Lie group theory to the equation under study, two dimensional Lie algebra is deduced. Using the obtained nontrivial Lie point symmetry, it is shown that the equation can be converted into a nonlinear fifth order ordinary differential equation of fractional order in the meaning of the Erdelyi-Kober fractional derivative operator. In addition, we construct some exact traveling solutions for the FMSK using the sub-equation method.

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