Trial equation method based on symmetry and applications to nonlinear equations arising in mathematical physics

DOI10.1007/s10701-010-9521-4zbMath1215.35142OpenAlexW2018520116MaRDI QIDQ537932

Cheng-Shi Liu

Publication date: 23 May 2011

Published in: Foundations of Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10701-010-9521-4

zbMATH Keywords

symmetryexact solutionreaction-diffusion equationtrial equation methodBurgers-KdV equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Traveling wave solutions (35C07) Methods of ordinary differential equations applied to PDEs (35A24) Symmetries, invariants, etc. in context of PDEs (35B06) Polynomial solutions to PDEs (35C11)

Related Items (8)

Qualitative and quantitative analysis of nonlinear dynamics by the complete discrimination system for polynomial method ⋮ Classification of traveling wave solutions to the modified form of the Degasperis-Procesi equation ⋮ Two model equations with a second degree logarithmic nonlinearity and their Gaussian solutions ⋮ Generalized trial equation method and its applications toDuffing and Poisson--Boltzmann equations ⋮ The classification of the single traveling wave solutions to \((1+1)\) dimensional Gardner equation with variable coefficients ⋮ The construction of solutions to Zakharov-Kuznetsov equation with fractional power nonlinear terms ⋮ Generalized system of trial equation methods and their applications to biological systems ⋮ Exact dynamical behavior for a dual Kaup-Boussinesq system by symmetry reduction and coupled trial equations method

Cites Work

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• Canonical-like transformation method and exact solutions to a class of diffusion equations
• High-order compact solution of the one-dimensional heat and advection-diffusion equations
• Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations
• Traveling-wave solutions for Korteweg-de Vries-Burgers equations through factorizations
• Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics
• Single and multi-solitary wave solutions to a class of nonlinear evolution equations
• Classification of All Single Travelling Wave Solutions to Calogero–Degasperis–Focas Equation
• Nonlinear Second Order Ode's: Factorizations and Particular Solutions
• CLASSIFICATION OF ALL ENVELOPE TRAVELING WAVE SOLUTIONS TO (2+1)-DIMENSIONAL DAVEY–STEWARTSON EQUATION
• SOLVING THE GENERALIZED BURGERS–KdV EQUATION BY A COMBINATION METHOD
• Representations and Classification of Traveling Wave Solutions to sinh-Gördon Equation

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