The extended hyperbolic functions method and new exact solutions to the Zakharov equations

DOI10.1016/j.amc.2007.10.059zbMath1143.65083OpenAlexW1992580632MaRDI QIDQ929422

Yong Huang, Yadong Shang, Wen-Jun Yuan

Publication date: 17 June 2008

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

Full work available at URL: https://doi.org/10.1016/j.amc.2007.10.059

zbMATH Keywords

periodic wave solutionssolitary wave solutionsexplicit and exact solutions

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (13)

New soliton solutions to the fractional perturbed nonlinear Schrodinger equation with power law nonlinearity ⋮ Exact periodic wave, bisoliton, and various breather solutions for the Zakharov equations ⋮ New soliton solutions of the generalized Zakharov equations using He's variational approach ⋮ The first-integral method and abundant explicit exact solutions to the Zakharov equations ⋮ New Jacobi elliptic function solutions for the Zakharov equations ⋮ EXPLICIT AND EXACT SOLUTIONS TO THE MODIFIED BENJAMIN-BONA-MAHONY EQUATION ⋮ A direct method for constructing the traveling wave solutions of a modified generalized Vakhnenko 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 \((G'/G,1/G)\)-expansion method and its application to travelling wave solutions of the Zakharov equations ⋮ Numerical solution of the generalized Zakharov equation by homotopy analysis method ⋮ A series of abundant exact travelling wave solutions for a modified generalized Vakhnenko equation using auxiliary equation method ⋮ Note on exact solutions for a class of nonlinear diffusion equations

Uses Software

• RAEEM

Cites Work

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• RAEEM: A Maple package for finding a series of exact traveling wave solutions for nonlinear evolution equations
• Methods of judging shape of solitary wave and solution formulae for some evolution equations with nonlinear terms of high order.
• Generalized method and its application in the higher-order nonlinear Schrödinger equation in nonlinear optical fibres.
• Exact solitary wave solutions of nonlinear wave equations.
• Exact travelling wave solutions of nonlinear evolution equations in (1+1) and (2+1) dimensions
• Explicit and exact solutions for generalized long-short wave resonance equations with strong nonlinear term
• Link between solitary waves and projective Riccati equations
• Complex Tanh-Function Expansion Method and Exact Solutions to Two Systems of Nonlinear Wave Equations

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