New exact travelling wave solutions for the \(K(2,2)\) equation with osmosis dispersion

DOI10.1016/j.amc.2009.04.073zbMath1203.35258arXiv0908.0914OpenAlexW1499799974MaRDI QIDQ609262

Xinghua Fan, Jiangbo Zhou, Lixin Tian

Publication date: 30 November 2010

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

Full work available at URL: https://arxiv.org/abs/0908.0914

zbMATH Keywords

bifurcation methodtravelling wave solution\(K(2,2)\) equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50) Software, source code, etc. for problems pertaining to partial differential equations (35-04) Traveling wave solutions (35C07) Soliton solutions (35C08)

Related Items (7)

New exact explicit peakon and smooth periodic wave solutions of the \(K(3,2)\) equation ⋮ Exact traveling wave solutions of explicit type, implicit type, and parametric type for \(K(m, n)\) equation ⋮ Single peak solitary wave and compacton solutions of the generalized two-component Hunter-Saxton system ⋮ Bifurcations and Single Peak Solitary Wave Solutions of an Integrable Nonlinear Wave Equation ⋮ Effects of Quadratic Singular Curves in Integrable Equations ⋮ Single peak solitary wave solutions for the osmosis \(K(2,2)\) equation under inhomogeneous boundary condition ⋮ Nonuniform continuity of the osmosis \(K(2, 2)\) equation

Uses Software

• Maple

Cites Work

• The bifurcation and peakon for \(K(2, 2)\) equation with osmosis dispersion
• Modified nonlinearly dispersive \(mK(m,n,k)\) equations: I. New compacton solutions and solitary pattern solutions
• Modified nonlinearly dispersive \(mK(m,n,k)\) equations: II. Jacobi elliptic function solutions
• 1-soliton solution of the \(K(m,n)\) equation with generalized evolution
• Bifurcations of travelling wave solutions for the \(mK(n, n)\) equation
• Variational approach to solitons of nonlinear dispersive \(K(m, n)\) equations
• Exp-function method for nonlinear wave equations
• Compactons and solitary patterns structures for variants of the KdV and the KP equations
• New exact solutions for modified nonlinear dispersive equations \(mK(m,n)\) in higher dimensions spaces.
• General compactons solutions and solitary patterns solutions for modified nonlinear dispersive equations \(mK(n,n)\) in higher dimensional spaces
• Homotopy perturbation method for bifurcation of nonlinear problems
• Compact and noncompact structures for a variant of KdV equation in higher dimensions
• New exact solitary-wave solutions for the \(K(2, 2, 1)\) and \(K(3, 3, 1)\) equations
• Construction of solitary solution and compacton-like solution by variational iteration method
• Compactons: Solitons with finite wavelength
• SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS

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