A generalized auxiliary equation method and its application to \((2+1)\)-dimensional Korteweg-de Vries equations

DOI10.1016/j.camwa.2006.12.046zbMath1143.35363OpenAlexW2124612096MaRDI QIDQ928801

Sheng Zhang

Publication date: 11 June 2008

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2006.12.046

zbMATH Keywords

soliton-like solutionsgeneralized auxiliary equation methodJacobi elliptic wave function-like solutionstriangular-like solutionsWeierstrass elliptic doubly-like periodic solutions

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Soliton equations (35Q51) Solutions to PDEs in closed form (35C05) Software, source code, etc. for problems pertaining to partial differential equations (35-04)

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Cites Work

• Unnamed Item
• The modified extended Fan sub-equation method and its application to the \((2+1)\)-dimensional Broer-Kaup-Kupershmidt equation
• Exact solutions to the double sinh-Gordon equation by the tanh method and a variable separated ODE method
• Exp-function method for nonlinear wave equations
• The periodic wave solutions for the \((2 + 1)\)-dimensional Konopelchenko-Dubrovsky equations
• Exact periodic and solitary waves and their interactions for the \((2+1)\)-dimensional KdV equation
• A further improved extended fan sub-equation method and its application to the \((3+1)\)-dimensional Kadomstev-Petviashvili equation
• A new auxiliary equation and exact travelling wave solutions of nonlinear equations
• Variational principles for some nonlinear partial differential equations with variable coefficients
• New exact travelling wave solutions for the Kawahara and modified Kawahara equations
• Fission and fusion of localized coherent structures for a \((2+1)\)-dimensional KdV equation
• An algebraic method exactly solving two high-dimensional nonlinear evolution equations
• Exact travelling wave solutions of the Whitham-Broer-Kaup and Broer-Kaup-Kupershmidt equations
• The solution of KdV and mKdV equations using Adomian Padé approximation
• Homotopy perturbation method for bifurcation of nonlinear problems
• Periodic wave solutions to a coupled KdV equations with variable coefficients
• Auxiliary equation method for solving nonlinear partial differential equations
• A note on the auxiliary equation method for solving nonlinear partial differential equations
• Exact solutions for a compound KdV-Burgers equation
• A simple transformation for nonlinear waves.
• The tanh and the sine-cosine methods for the complex modified KdV and the generalized KdV equations
• Variational approach to \((2+1)\)-dimensional dispersive long water equations
• Application of homotopy perturbation method to nonlinear wave equations
• Weierstrass semi-rational expansion method and new doubly periodic solutions of the generalized Hirota-Satsuma coupled KdV system
• A unified rational expansion method to construct a series of explicit exact solutions to nonlinear evolution equations
• Revisitation of the localized excitations of the (2+1)-dimensional KdV equation
• Solitary wave solutions of nonlinear wave equations
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• The Painlevé property for partial differential equations
• Generalized dromion solutions of the (2+1)-dimensional KdV equation
• Infinitely many Lax pairs and symmetry constraints of the KP equation
• On the spectral transform of a Korteweg-de Vries equation in two spatial dimensions
• A Series of Soliton-like and Double-like Periodic Solutions of a (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Vesselov Equation
• SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS
• Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations

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