Bifurcations of travelling wave solutions for the \(mK(n, n)\) equation

DOI10.1016/j.cnsns.2007.06.006zbMath1221.35336OpenAlexW2059603777MaRDI QIDQ718789

Qing Meng, Bin He, Yao Long, Wei-Guo Rui

Publication date: 24 September 2011

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2007.06.006

zbMATH Keywords

solitary waveperiodic waveperiodic cusp waven)\) equationkink and anti-kink wave\(mK(n

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Soliton equations (35Q51) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (5)

New exact travelling wave solutions for the \(K(2,2)\) equation with osmosis dispersion ⋮ Some new soliton-like solutions and periodic wave solutions with loop or without loop to a generalized KdV equation ⋮ Application of the integral bifurcation method for solving modified Camassa-Holm and Degasperis-Procesi equations ⋮ New soliton-like solutions and compacton-like periodic wave solutions of parametric type to a nonlinear dispersive equation ⋮ Soliton and periodic wave solutions to the osmosis \(K(2,2)\) equation

Cites Work

• 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
• Compact and noncompact dispersive patterns
• New exact solutions for modified nonlinear dispersive equations \(mK(m,n)\) in higher dimensions spaces.
• Compact and noncompact structures for a variant of KdV equation in higher dimensions
• General compactons solutions for the focusing branch of the nonlinear dispersive \(K(n,n)\) equations in higher-dimensional spaces
• General solutions with solitary patterns for the defocusing branch of the nonlinear dispersive \(K(n,n)\) equations in higher dimensional spaces
• Compactons: Solitons with finite wavelength
• Smooth and non-smooth traveling waves in a nonlinearly dispersive equation

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