The generalized projective Riccati equations method for solving nonlinear evolution equations in mathematical physics
type: Item
instance of: scholarly article
title: The generalized projective Riccati equations method for solving nonlinear evolution equations in mathematical physics
zbMATH Open document ID: 1472.35344
DOI: 10.1155/2014/259190
author: K. A. E. Alurrfi
author: Elsayed M. E. Zayed
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35C07
zbMATH DE Number: 7022021
zbMATH Keywords: Riccati equations
zbMATH Keywords: Pochhammer-Chree equation, nonlinear Burgers equation
zbMATH Keywords: nonlinear Zakharov-Kuznetsov equation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/259190
OpenAlex ID: W1987687282
Wikidata QID: Q59037078
cites work: Q3995225
cites work: Exact solutions for the nonlinear Schrödinger equation with variable coefficients using the generalized extended tanh-function, the sine-cosine and the exp-function methods
cites work: Group analysis and modified extended tanh-function to find the invariant solutions and soliton solutions for nonlinear Euler equations
cites work: The extended tanh method for abundant solitary wave solutions of nonlinear wave equations
cites work: New exact travelling wave solutions using modified extended tanh-function method
cites work: Extended tanh-function method and its applications to nonlinear equations
cites work: Q5505272
cites work: Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
cites work: The Painlevé property for partial differential equations
cites work: Bäcklund transformations and their applications
cites work: Exp-function method for nonlinear wave equations
cites work: New solitonary solutions for the MBBM equations using Exp-function method
cites work: Application of exp-function method to high-dimensional nonlinear evolution equation
cites work: Application of the exp-function method for nonlinear differential-difference equations
cites work: Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to \((1+1)\)-dimensional dispersive long wave equation
cites work: Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
cites work: Jacobi elliptic function solutions for two variant Boussinesq equations
cites work: On exact solutions of the nonlinear Schrödinger equations in optical fiber
cites work: New explicit exact solutions for the generalized coupled Hirota-Satsuma KdV system
cites work: The \((\frac{G'}{G})\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
cites work: A generalized \((\frac{G'}{G})\)-expansion method for the mKdV equation with variable coefficients
cites work: The (\(\frac{G'}{G})\)-expansion method and its applications to some nonlinear evolution equations in the mathematical physics
cites work: Application of the \((\frac{G'}{G})\)-expansion method for nonlinear evolution equations
cites work: Application of the extended \(\frac{G'}{G}\)-expansion method to solve the Pochhammer-Chree equations
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 \((G'/G,1/G)\)-expansion method and its application to travelling wave solutions of the Zakharov equations
cites work: The two-variable \((G'/G, 1/G)\)-expansion method for solving the nonlinear KdV-mKdV equation
cites work: Traveling wave solutions of the nonlinear \((3 + 1)\)-dimensional Kadomtsev-Petviashvili equation using the two variables \((G/G, 1/G)\)-expansion method
cites work: Link between solitary waves and projective Riccati equations
cites work: On the integrability of systems of nonlinear ordinary differential equations with superposition principles
cites work: Exact solitary wave solutions of nonlinear wave equations.
cites work: Generalized method and its application in the higher-order nonlinear Schrödinger equation in nonlinear optical fibres.
cites work: The tanh-coth and the sine-cosine methods for kinks, solitons, and periodic solutions for the Pochhammer-Chree equations
cites work: Travelling wave solutions of generalized forms of Burgers, Burgers-KdV and Burgers-Huxley equations
cites work: Growth rate of transverse instabilities of solitary pulse solutions to a family of modified Zakharov-Kuznetsov equations
cites work: Travelling wave solutions for the generalized Zakharov-Kuznetsov equation with higher-order nonlinear terms
description: scientific article; zbMATH DE number 7022021