Bifurcations of traveling wave solutions for Zhiber--Shabat equation

DOI10.1016/j.na.2006.06.024zbMath1222.35179OpenAlexW2090092041MaRDI QIDQ880329

Jianwei Shen, Liang Gao, Wei Xu, Ya-Ning Tang

Publication date: 15 May 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.06.024

zbMATH Keywords

traveling wave solutionsbifurcation theory of dynamical systemsZhiber--Shabat equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Bifurcations in context of PDEs (35B32) Traveling wave solutions (35C07)

Related Items (9)

Qualitative behavior and exact travelling wave solutions of the Zhiber-Shabat equation ⋮ A TUTORIAL INTRODUCTION TO THE TWO-SCALE FRACTAL CALCULUS AND ITS APPLICATION TO THE FRACTAL ZHIBER–SHABAT OSCILLATOR ⋮ A improved F-expansion method and its application to the Zhiber-Shabat equation ⋮ Bounded traveling waves of the Burgers-Huxley equation ⋮ Bell-polynomial approach and soliton solutions for the Zhiber-Shabat equation and (2+1)-dimensional Gardner equation with symbolic computation ⋮ Lie group analysis and dynamical behavior for classical Boussinesq-Burgers system ⋮ Explicit exact traveling wave solutions and bifurcations of the generalized combined double \(\sinh\)-\(\cosh\)-Gordon equation ⋮ An analysis of the Zhiber-Shabat equation including Lie point symmetries and conservation laws ⋮ New exact bounded travelling wave solutions for the Zhiber-Shabat equation

Cites Work

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• New exact solutions for the sinh-Gordon equation
• Bifurcations of travelling wave solutions in a new integrable equation with peakon and compactons
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• A sinh-Gordon equation expansion method to construct doubly periodic solutions for nonlinear differential equations.
• A direct method for solving sine-Gordon type equations
• Peakons of the Camassa-Holm equation
• Bifurcations of smooth and non-smooth travelling wave solutions in the generalized Camassa-Holm equation
• New compacton-like and solitary patterns-like solutions to nonlinear wave equations with linear dispersion terms
• Lie transformations, nonlinear evolution equations, and Painlevé forms
• Link between solitary waves and projective Riccati equations
• Compactons: Solitons with finite wavelength

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