HOMOCLINIC MANIFOLDS, CENTER MANIFOLDS AND EXACT SOLUTIONS OF FOUR-DIMENSIONAL TRAVELING WAVE SYSTEMS FOR TWO CLASSES OF NONLINEAR WAVE EQUATIONS

DOI10.1142/S0218127411028581zbMath1210.34061MaRDI QIDQ2994878

Yi Zhang, Ji-Bin Li

Publication date: 29 April 2011

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

center manifoldembedded solitonquasi-periodic wave solutiongap solitonbifurcation of equilibriumhomoclinic manifoldKdV-Sawada-Kotera-Ramani equationLax kdv5 equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Bifurcation theory for ordinary differential equations (34C23) Explicit solutions, first integrals of ordinary differential equations (34A05) Invariant manifolds for ordinary differential equations (34C45) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Soliton solutions (35C08)

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Exact solitary wave and periodic wave solutions of a class of higher-order nonlinear wave equations, Lie symmetries, integrable properties and exact solutions to the variable-coefficient nonlinear evolution equations, Classification and bifurcation of a class of second-order ODEs and its application to nonlinear PDEs, Exact solutions in invariant manifolds of some higher-order models describing nonlinear waves, Quasi-periodic wave solutions and two-wave solutions of the KdV-Sawada-Kotera-Ramani equation, Exact solitary wave and quasi-periodic wave solutions of the KdV-Sawada-Kotera-Ramani equation, Series solutions and bifurcation of traveling waves in the Benney-Kawahara-Lin equation

Cites Work

• Solitons and periodic solutions for the fifth-order KdV equation with the Exp-function method
• Supersymmetric KdV-Sawada-Kotera-Ramani equation and its quasi-periodic wave solutions
• Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method
• Detection of symmetric homoclinic orbits to saddle-centres in reversible systems
• The integrable KdV6 equations: Multiple soliton solutions and multiple singular soliton solutions
• Dark Equations
• Higher‐order Painlevé Equations in the Polynomial Class I. Bureau Symbol P2
• Dynamics of Embedded Solitons in the Extended Korteweg–de Vries Equations
• A new integrable generalization of the Korteweg–de Vries equation
• Integrals of nonlinear equations of evolution and solitary waves
• Embedded solitons: A new type of solitary wave