The Bäcklund transformations and abundant exact explicit solutions for a general nonintegrable nonlinear convection-diffusion equation
type: Item
instance of: scholarly article
title: The Bäcklund transformations and abundant exact explicit solutions for a general nonintegrable nonlinear convection-diffusion equation
zbMATH Open document ID: 1254.35045
DOI: 10.1155/2012/489043
author: Yong Huang
author: Yadong Shang
published in: Abstract and Applied Analysis
publication date: 2012-01-05T00:00:00Z
review text: Summary: The Bäcklund transformations and abundant exact explicit solutions for a class of nonlinear wave equations are obtained by the extended homogeneous balance method. These solutions include the solitary wave solution of rational function, the solitary wave solutions, singular solutions, and the periodic wave solutions of triangle function type. In addition to rederiving some known solutions, some entirely new exact solutions are also established. Explicit and exact particular solutions of many well-known nonlinear evolution equations which are of important physical significance, such as Kolmogorov-Petrovskii-Piskunov equation, FitzHugh-Nagumo equation, Burgers-Huxley equation, Chaffee-Infante reaction diffusion equation, Newell-Whitehead equation, Fisher equation, Fisher-Burgers equation, and an isothermal autocatalytic system, are obtained as special cases.
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 58J72
Mathematics Subject Classification ID: 35C08
zbMATH DE Number: 5994552
zbMATH Keywords: extended homogeneous balance method
zbMATH Keywords: solitary wave solution
zbMATH Keywords: periodic wave solutions
zbMATH Keywords: Chaffee-Infante reaction diffusion equation
zbMATH Keywords: Newell-Whitehead equation
zbMATH Keywords: Kolmogorov-Petrovskii-Piskunov equation
zbMATH Keywords: FitzHugh-Nagumo equation
zbMATH Keywords: Burgers-Huxley equation
Wikidata QID: Q58695316
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/489043
OpenAlex ID: W2013200902
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description: scientific article; zbMATH DE number 5994552