New interaction solutions to the KdV equation

Lü, DaZhao; Cui, YanYing; Wang, Xiaojing; Nie, Chuanhui

doi:10.1016/j.physleta.2009.10.056

Cited by 5 publications

(1 citation statement)

References 17 publications

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“…Recently, exact solution of coupled KdV equations based on Kudryashov technique demonstrated by [30]. Numerous approaches have been handled to these problems such as: finite difference scheme [31], ( ) ¢ G G -expansion method, finite volume scheme [32], homotopy analysis method [33], finite element scheme [34], decomposition method [35], spectral method [36], Wronskian form expansion method [37] Exp-function method, canonical formulation of Whitham's variational principle [38], residual power series method [39], tanh function method, variational iteration method [40], inverse scattering transform [41] and reduced differential transformation method [42].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of Korteweg–de Vries-Burgers equation by the modified variational iteration algorithm-II arising in shallow water waves

2020

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In this paper, an effective modification of variational iteration algorithm-II is presented for the numerical solution of the Korteweg–de Vries-Burgers equation, Burgers equation and Kortewege–de Vries equation. In this modification, an auxiliary parameter is introduced which make sure the convergence of the standard algorithm-II. In order to assess the precision of the solutions, numerical computations obtained from the time evaluation of the solutions of the Kortewege–de Vries-Burgers equation with different values for dispersion and diffusion coefficients, show that the proposed algorithm converges rapidly, yields accurate results and offers better accuracy and robustness in comparison with other previous numerical methods. Furthermore, the method can be readily implemented for illuminating viably an enormous number of nonlinear differential equations with better accuracy. Furthermore, any transformation, weak nonlinearity assumption to find an explicit solution or any discretization to find the numerical solution is not necessary for this proposed algorithm.

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Section: Introductionmentioning

confidence: 99%

Numerical solution of Korteweg–de Vries-Burgers equation by the modified variational iteration algorithm-II arising in shallow water waves

2020

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New interaction solutions of (3+1)-dimensional Zakharov–Kuznetsov equation

et al. 2013

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Soliton solutions for a variable-coefficient Korteweg–de Vries equation in fluids and plasmas

Jiang¹,

Tian²,

Liu³

et al. 2010

Phys. Scr.

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In this paper, we investigate a variable-coefficient Korteweg–de Vries (vc-KdV) equation, which can be used to describe the propagation of nonlinear waves in fluids, plasmas and other fields. Through the rational transformation and Hirota method, new soliton solutions to the vc-KdV equation are derived. On the basis of those soliton solutions, three types of collisions are obtained: overtaking collision between two unidirectional solitons, head-on collision between two bidirectional ones and collision between moving and stationary solitons. These collisions are proved to be elastic through asymptotic analysis, and figures are plotted which show that they are indeed elastic except for a phase shift.

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New interaction solutions to the KdV equation

Cited by 5 publications

References 17 publications

Numerical solution of Korteweg–de Vries-Burgers equation by the modified variational iteration algorithm-II arising in shallow water waves

Numerical solution of Korteweg–de Vries-Burgers equation by the modified variational iteration algorithm-II arising in shallow water waves

New interaction solutions of (3+1)-dimensional Zakharov–Kuznetsov equation

Soliton solutions for a variable-coefficient Korteweg–de Vries equation in fluids and plasmas

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