On explicit exact solutions and conservation laws for time fractional variable - coefficient coupled Burger’s equations

Kaur, Jaskiran; Gupta, Rajesh Kumar; Kumar, Sachin

doi:10.1016/j.cnsns.2019.105108

Cited by 18 publications

(3 citation statements)

References 37 publications

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“…Therefore, research of variable coefficient equations is of even more physical significance. [29][30][31] When δ (t) = 1, Eq. ( 1) is the third flow of the NLS structure, and this nonlinear evolution equation can be used to describe important models in physics, fibre optics and other engineering disciplines.…”

Section: Introductionmentioning

confidence: 99%

Darboux transformation, infinite conservation laws, and exact solutions for the nonlocal Hirota equation with variable coefficients

Liu 刘,

Yan 闫,

Jin 金

et al. 2023

Chinese Phys. B

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This article presents the construction of a nonlocal Hirota equation with variable coefficient and its Darboux transformation. Using zero-seed solutions, 1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation, along with the expression for N-soliton solutions. The influence of coefficient functions on the solutions is investigated by choosing different coefficient functions, and the dynamics of the solutions are analyzed. For the first time, this article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations. The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.

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Section: Introductionmentioning

confidence: 99%

Darboux transformation, infinite conservation laws, and exact solutions for the nonlocal Hirota equation with variable coefficients

Liu 刘,

Yan 闫,

Jin 金

et al. 2023

Chinese Phys. B

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“…The coupled system is composed of two or more differential equations (include ordinary differential equations, partial differential equations fractional partial differential equations, and stochastic partial differential equations) [1][2][3]. It is a very important class of mathematical and physical equations.…”

Section: Introductionmentioning

confidence: 99%

Classification of All Single Traveling Wave Solutions of Fractional Coupled Boussinesq Equations via the Complete Discrimination System Method

Han

2021

Advances in Mathematical Physics

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In this paper, the complete discrimination system method is used to construct the exact traveling wave solutions for fractional coupled Boussinesq equations in the sense of conformable fractional derivatives. As a result, we get the exact traveling wave solutions of fractional coupled Boussinesq equations, which include rational function solutions, Jacobian elliptic function solutions, implicit solutions, hyperbolic function solutions, and trigonometric function solutions. Finally, the obtained solution is compared with the existing literature.

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“…It is well known that the fractional partial differential equations (FPDEs) [1][2][3][4][5][6][7][8][9][10][11] have received considerable attention [12][13][14][15][16][17][18][19] due to their wide use to describe various complex physical phenomena in the domain of science and engineering. Among the research of the FPDEs, analyzing the bifurcations and the exact traveling wave solutions of FPDEs have been widely investigated as an important subject.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and exact solutions for the ($2+1$)-dimensional conformable time-fractional Zoomeron equation

Han

2020

Adv Differ Equ

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In this paper, the bifurcation and new exact solutions for the ($2+1$ 2 + 1 )-dimensional conformable time-fractional Zoomeron equation are investigated by utilizing two reliable methods, which are generalized $(G'/G)$ ( G ′ / G ) -expansion method and the integral bifurcation method. The exact solutions of the ($2+1$ 2 + 1 )-dimensional conformable time-fractional Zoomeron equation are obtained by utilizing the generalized $(G'/G)$ ( G ′ / G ) -expansion method, these solutions are classified as hyperbolic function solutions, trigonometric function solutions, and rational function solutions. Giving different parameter conditions, many integral bifurcations, phase portraits, and traveling wave solutions for the equation are obtained via the integral bifurcation method. Graphical representations of different kinds of the exact solutions reveal that the two methods are of significance for constructing the exact solutions of fractional partial differential equation.

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On explicit exact solutions and conservation laws for time fractional variable - coefficient coupled Burger’s equations

Cited by 18 publications

References 37 publications

Darboux transformation, infinite conservation laws, and exact solutions for the nonlocal Hirota equation with variable coefficients

Darboux transformation, infinite conservation laws, and exact solutions for the nonlocal Hirota equation with variable coefficients

Classification of All Single Traveling Wave Solutions of Fractional Coupled Boussinesq Equations via the Complete Discrimination System Method

Bifurcation and exact solutions for the ($2+1$)-dimensional conformable time-fractional Zoomeron equation

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