Some new traveling wave solutions of the nonlinear reaction diffusion equation by using the improved \((G'/G)\)-expansion method
type: Item
instance of: scholarly article
title: Some new traveling wave solutions of the nonlinear reaction diffusion equation by using the improved \((G'/G)\)-expansion method
zbMATH Open document ID: 1264.35123
DOI: 10.1155/2012/871724
author: Hasibun Naher
author: Farah Aini Abdullah
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: We construct new exact traveling wave solutions involving free parameters of the nonlinear reaction diffusion equation by using the improved \((G'/G)\)-expansion method. The second-order linear ordinary differential equation with constant coefficients is used in this method. The obtained solutions are presented by the hyperbolic and the trigonometric functions. The solutions become in special functional form when the parameters take particular values. It is important to reveal that our solutions are in good agreement with the existing results.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 6173660
Wikidata QID: Q58912591
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/871724
OpenAlex ID: W1991419399
cites work: A class of exact, periodic solutions of nonlinear envelope equations
cites work: Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
cites work: Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
cites work: Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equa\-tion
cites work: Bäcklund transformations and their applications
cites work: Bäcklund transformation and new exact solutions of the Sharma-Tasso-Olver equation
cites work: New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water
cites work: Exact solutions to KdV6 equation by using a new approach of the projective Riccati equation method
cites work: A sub-ODE method for finding exact solutions of a generalized KdV-mKdV equation with high-order nonlinear terms
cites work: Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics
cites work: On the solitary wave solutions for nonlinear Hirota-Satsuma coupled KdV equations
cites work: The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations
cites work: Exact solutions of coupled nonlinear Klein-Gordon equations
cites work: Analytic solutions of the (2 + 1)-dimensional nonlinear evolution equations using the sine-cosine method
cites work: Application of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equation
cites work: Exp-function method for nonlinear wave equations
cites work: Application of the exp-function method for solving nonlinear reaction-diffusion equations arising in mathematical biology
cites work: New traveling wave solutions of the higher dimensional nonlinear partial differential equation by the Exp-function method
cites work: The extended tanh method and the exp-function method to solve a kind of nonlinear heat equation
cites work: Application of the exp-function method to nonlinear lattice differential equations for multi-wave and rational solutions
cites work: A new (2+1)-dimensional Korteweg–de Vries equation and its extension to a new (3+1)-dimensional Kadomtsev–Petviashvili equation
cites work: Exact solutions of the generalized Benjamin-Bona-Mahony equation
cites work: Soliton perturbation theory for the quadratic nonlinear Klein-Gordon equation
cites work: Soliton perturbation theory for phi-four model and nonlinear Klein-Gordon equations
cites work: Topological and non-topological solitons of the generalized Klein-Gordon equations
cites work: Topological and non-topological solitons of nonlinear Klein-Gordon equations by He's semi-inverse variational principle
cites work: Q3559562
cites work: Topological and non-topological solitons of the Klein-Gordon equations in \(1+2\) dimensions
cites work: Q3083663
cites work: On a new integral transform and differential equations
cites work: Some new iterative methods for nonlinear equations
cites work: Mathematical transform of traveling-wave equations and phase aspects of quantum interaction
cites work: The extended \(F\)-expansion method and its application for a class of nonlinear evolution equations
cites work: An analytic solution for a Vasicek interest rate convertible bond model
cites work: A new general iterative method for solution of a new general system of variational inclusions for nonexpansive semigroups in Banach spaces
cites work: An iteration method generating analytical solutions for Blasius problem
cites work: The \((\frac{G'}{G})\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
cites work: Exact travelling wave solutions of some nonlinear equations by \((\frac{G'}{G})\)-expansion method
cites work: Application of the \((\frac{G'}{G})\)-expansion method for nonlinear evolution equations
cites work: New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized \big(\frac{G^{\prime}}{G}\big) -expansion method
cites work: The \((G'/G)\)-expansion method for abundant traveling wave solutions of Caudrey-Dodd-Gibbon equation
cites work: Constructing of exact solutions to the KdV and Burgers equations with power-law nonlinearity by the extended \((\frac{G'}{G})\)-expansion method
cites work: The extended \(\left( \frac {G^{\prime}}{G}\right)\)-expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations
cites work: Applications of an extended \((G'/G)\)-expansion method to find exact solutions of nonlinear PDEs in mathematical physics
cites work: An improved (G′/G)-expansion method for solving nonlinear evolution equations
cites work: The improved \((\frac{G'}{G})\)-expansion method for solving (3+1)-dimensional potential-YTSF equation
cites work: Q2932171
cites work: Application of the improved (\(\frac{G'}{G}\))-expansion method for the variant Boussinesq equations
description: scientific article; zbMATH DE number 6173660