New Exact Travelling Wave Solutions for Zakharov–Kuznetsov Equation

Ma, Hongcai; Yu, Yang; Ge, Dong-Jie

doi:10.1088/0253-6102/51/4/07

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…A Lie point symmetry for Equation ( 6) is a transformation (7) that leaves (6) invariant. From (7) one can obtain the associated vector field which is given by…”

Section: Lie Symmetriesmentioning

confidence: 99%

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Lie Symmetries and Low-Order Conservation Laws of a Family of Zakharov-Kuznetsov Equations in 2 + 1 Dimensions

et al. 2020

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In this work, we study a generalised (2+1) equation of the Zakharov–Kuznetsov (ZK)(m,n,k) equation involving three arbitrary functions. From the point of view of the Lie symmetry theory, we have derived all Lie symmetries of this equation depending on the arbitrary functions. Line soliton solutions have also been obtained. Moreover, we study the low-order conservation laws by applying the multiplier method. This family of equations is rich in Lie symmetries and conservation laws. Finally, when the equation is expressed in potential form, it admits a variational structure in the case when two of the arbitrary functions are linear. In addition, the corresponding Hamiltonian formulation is presented.

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“…A Lie point symmetry for Equation ( 6) is a transformation (7) that leaves (6) invariant. From (7) one can obtain the associated vector field which is given by…”

Section: Lie Symmetriesmentioning

confidence: 99%

“…where a, b, c are arbitrary constants while m, n and k are positive integers [6][7][8]. • ZK(m, n, k) equation with generalised evolution and time-dependent coefficients (u l ) t + a(t)(u m…”

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confidence: 99%

Lie Symmetries and Low-Order Conservation Laws of a Family of Zakharov-Kuznetsov Equations in 2 + 1 Dimensions

et al. 2020

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The exact solutions of Schrödinger–Hirota equation based on the auxiliary equation method

Du,

Yin,

Pang

2024

Opt Quant Electron

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Analytical study of nonlinear water wave equations for their fractional solution structures

et al. 2022

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This paper examines the three-dimensional nonlinear time-fractional water wave equations for their analytical wave solutions. These are the equations of the names [Formula: see text]-Zakharov–Kuznetsov–Burgers equation and [Formula: see text]-Yu–Toda–Sasa–Fukuyama equation. The obtained wave solutions are in the form of kink, periodic and singular waves by utilizing the [Formula: see text]-expansion approach. The aforesaid solutions are verified and demonstrated graphically via symbolic soft computations.

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New Exact Travelling Wave Solutions for Zakharov–Kuznetsov Equation

Abstract: In this paper, the nonlinear dispersive Zakharov-Kuznetsov equation is solved by using the generalized auxiliary equation method. As a result, new solitary pattern, solitary wave and singular solitary wave solutions are found.

Cited by 5 publications

References 12 publications

Lie Symmetries and Low-Order Conservation Laws of a Family of Zakharov-Kuznetsov Equations in 2 + 1 Dimensions

Lie Symmetries and Low-Order Conservation Laws of a Family of Zakharov-Kuznetsov Equations in 2 + 1 Dimensions

The exact solutions of Schrödinger–Hirota equation based on the auxiliary equation method

Analytical study of nonlinear water wave equations for their fractional solution structures

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