A new auxiliary equation method for finding travelling wave solutions to KdV equation

DOI10.1007/s10483-010-1327-zzbMath1202.37088OpenAlexW1981188573MaRDI QIDQ605214

Jing Pang, Chun-quan Bian, Lu Chao

Publication date: 23 November 2010

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10483-010-1327-z

zbMATH Keywords

KdV equationhomogeneous balance methodauxiliary equation methodtravelling wave solution

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05)

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Cites Work

• Unnamed Item
• The \((\frac{G'}{G})\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
• A generalized new auxiliary equation method and its applications to nonlinear partial differential equations
• A generalized \((\frac{G'}{G})\)-expansion method for the mKdV equation with variable coefficients
• Application of the \((\frac{G'}{G})\)-expansion method for nonlinear evolution equations
• A generalized \((\frac{G'}{G})\)-expansion method and its applications
• Solving two fifth order strong nonlinear evolution equations by using the \((\frac{G}{G'})\)-expansion method
• Application of exp-function method for \((3+1)\)-dimensional nonlinear evolution equations
• Optimal error estimates for Fourier spectral approximation of the generalized KdV equation
• Existence of traveling wave solutions for a nonlinear dissipative-dispersive equation
• Method of lines solution of the Korteweg-de Vries equation
• Distinct variants of the KdV equation with compact and noncompact structures.
• Compactons, solitons and periodic solutions for variants of the KdV and the KP equations
• A sine-cosine method for handling nonlinear wave equations
• The tanh method for traveling wave solutions of nonlinear equations
• The extended Fan's sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations