Journal ArticleDOI
Symmetry and similarity solutions of variable coefficients generalized Zakharov–Kuznetsov equation
Zhi-lian Yan,Xi-Qiang Liu +1 more
TLDR
A compatibility method of finding symmetry and similarity reduction of partial differential equations of Zakharov–Kuznetsov equation and can be applied to other nonlinear evolution equations in mathematical physics.About:
This article is published in Applied Mathematics and Computation.The article was published on 2006-09-01. It has received 46 citations till now. The article focuses on the topics: Partial differential equation & Similarity solution.read more
Citations
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Lie symmetry analysis to the time fractional generalized fifth-order KdV equation
TL;DR: It is shown that this equation can be reduced to an equation which is related to the Erdelyi–Kober fractional derivative, and this method can be applied to other nonlinear fractional partial differential equations.
Journal ArticleDOI
Application of Exp-function method for nonlinear evolution equations with variable coefficients
TL;DR: In this article, the Exp-function method with the aid of symbolic computational system Maple is used to obtain generalized solitary solutions and periodic solutions of a generalized Zakharov-Kuznetsov equation with variable coefficients.
Journal ArticleDOI
Travelling wave solutions for the generalized Zakharov–Kuznetsov equation with higher-order nonlinear terms
TL;DR: By means of two proper transformations, the generalized Zakharov–Kuznetsov (GZK) equation is transformed to an ordinary differential equation that is easy to solve and a rich variety of new exact travelling wave solutions are found.
Journal ArticleDOI
Nonlinear dust acoustic waves in a nonuniform magnetized complex plasma with nonthermal ions and dust charge variation
TL;DR: In this paper, a modified Zakhavov-Kusnetsov-Burgers (MZKB) equation was used to model the evolution of nonlinear DA solitary waves in a non-uniform magnetized dusty plasma.
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ANALYTICAL TREATMENT OF SOME PARTIAL DIFFERENTIAL EQUATIONS ARISING IN MATHEMATICAL PHYSICS BY USING THE Exp-FUNCTION METHOD
TL;DR: In this paper, the generalized solitary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics were obtained using the Exp-function method with the aid of symbolic computational system.
References
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Journal ArticleDOI
New similarity reductions of the Boussinesq equation
TL;DR: In this paper, some new similarity reductions of the Boussinesq equation, which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering, are presented.
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Painlevé equations: nonlinear special functions
TL;DR: In this paper, the authors discuss some of the remarkable properties which the Painleve equations possess including connection formulae, Backlund transformations associated discrete equations, and hierarchies of exact solutions.
Journal ArticleDOI
Exact solutions with solitons and periodic structures for the Zakharov–Kuznetsov (ZK) equation and its modified form
TL;DR: In this article, the authors study the Zakharov-Kuznetsov (ZK) equation and two of its modified forms and employ the sine-cosine algorithm to back up their analysis.
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Similarity solutions to non-linear partial differential equation of physical phenomena represented by the Zakharov-Kuznetsov equation
TL;DR: In this article, the authors analyzed the non-linear partial differential equation called the Zakharov-Kuznetsov equation via symmetry method as developed by S. Steinberg and showed that the symmetries form a finite dimensional vector Lie algebra.
Journal ArticleDOI
Symmetry Reductions and Explicit Solutions for a Generalized Zakharov?Kuznetsov Equation
Yan Zhi-lian,Liu Xi-Qiang +1 more
TL;DR: In this article, two types of symmetry of a generalized Zakharov?Kuznetsov equation are obtained via direct symmetry method by selecting suitable parameters occurring in the symmetries.