A series of abundant exact travelling wave solutions for a modified generalized Vakhnenko equation using auxiliary equation method

DOI10.1016/j.amc.2009.01.036zbMath1400.35203OpenAlexW2062174730MaRDI QIDQ1021493

Cong Wang, Bang-Qing Li, Yu-Lan Ma

Publication date: 8 June 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.01.036

zbMATH Keywords

Jacobi elliptic functionsoliton solutionauxiliary equation methodtravelling wave solutionmodified generalized Vakhnenko equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Solutions to PDEs in closed form (35C05) Traveling wave solutions (35C07) Soliton solutions (35C08)

Related Items (14)

Exact periodic, cusp, solitary and loop wave solutions of the EX-ROE ⋮ Simple equation method for nonlinear partial differential equations and its applications ⋮ Some new soliton-like solutions and periodic wave solutions with loop or without loop to a generalized KdV equation ⋮ Soliton solutions and other solutions to the \((4+1)\)-dimensional Davey-Stewartson-Kadomtsev-Petviashvili equation using modified extended mapping method ⋮ The \(N\)-loop soliton solutions for \((2+1)\)-dimensional Vakhnenko equation ⋮ New Jacobi elliptic function solutions for the Zakharov equations ⋮ Traveling magnetic wave motion in ferrites: impact of inhomogeneous exchange effects ⋮ A direct method for constructing the traveling wave solutions of a modified generalized Vakhnenko equation ⋮ Bifurcations and some new traveling wave solutions for the CH-\({\gamma}\) equation ⋮ New exact solutions to the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity via modified trigonometric function series method ⋮ New application of \((G'/G)\)-expansion method to a nonlinear evolution equation ⋮ The non-traveling wave solutions and novel fractal soliton for the \((2 + 1)\)-dimensional Broer-Kaup equations with variable coefficients ⋮ Some new Jacobi elliptic function solutions for the short-pulse equation via a direct symbolic computation method ⋮ A method for constructing nontraveling wave solutions for (1+1)-dimensional evolution equations

Uses Software

• ATFM

Cites Work

• Unnamed Item
• The \((\frac{G'}{G})\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
• Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method
• A generalized \((\frac{G'}{G})\)-expansion method for the mKdV equation with variable coefficients
• Some new solitary and travelling wave solutions of certain nonlinear diffusion-reaction equations using auxiliary equation method
• Application of the \((\frac{G'}{G})\)-expansion method for nonlinear evolution equations
• Exp-function method for constructing explicit and exact solutions of a lattice equation
• A further improved extended Fan sub-equation method for \((2+1)\)-dimensional breaking soliton equations
• The extended hyperbolic functions method and new exact solutions to the Zakharov equations
• New applications of developed Jacobi elliptic function expansion methods
• A new auxiliary equation and exact travelling wave solutions of nonlinear equations
• An automated \(\tanh\)-function method for finding solitary wave solutions to nonlinear evolution equations
• The periodic wave solutions for the Klein-Gordon-Schrödinger equations
• Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics
• A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation
• Auto-Bäcklund transformation and exact solutions for modified nonlinear dispersive \(mK(m,n)\) equations
• The \(N\)-soliton solution of the modified generalised Vakhnenko equation (a new nonlinear evolution equation).
• New exact travelling wave solutions for the Kawahara and modified Kawahara equations
• Travelling wave solutions in terms of special functions for nonlinear coupled evolution systems
• The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method.
• Periodic wave solutions to a coupled KdV equations with variable coefficients
• Auxiliary equation method for solving nonlinear partial differential equations
• Solitary wave solutions for variant Boussinesq equations
• A simple transformation for nonlinear waves.
• Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics
• New exact travelling wave solutions using modified extended tanh-function method
• Symbolic computation of exact solutions for a nonlinear evolution equation
• A new Riccati equation rational expansion method and its application to \((2+1)\)-dimensional Burgers equation
• The two loop soliton solution of the Vakhnenko equation
• High-frequency soliton-like waves in a relaxing medium
• Generalized hyperbolic-function method with computerized symbolic computation to construct the solitonic solutions to nonlinear equations of mathematical physics
• New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water
• Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
• Auto-Bäcklund transformation and similarity reductions for general variable coefficient KdV equations

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