scholarly journals Exact Solutions of Generalized Boussinesq-Burgers Equations and (2+1)-Dimensional Davey-Stewartson Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Isaiah Elvis Mhlanga ◽  
Chaudry Masood Khalique
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Travelling Wave ◽  
Lie Symmetry ◽  
Coupled Systems ◽  
Burgers Equations ◽  
Lie Symmetry Method ◽  
Symmetry Method

We study two coupled systems of nonlinear partial differential equations, namely, generalized Boussinesq-Burgers equations and (2+1)-dimensional Davey-Stewartson equations. The Lie symmetry method is utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the (2+1)-dimensional Davey-Stewartson equations.

scholarly journals Reductions and exact solutions of some nonlinear partial differential equations under four types of generalized conditional symmetries

1999 ◽  
Vol 41 (1) ◽  
pp. 1-40 ◽  
Author(s):  
Changzheng Qu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Dynamical Behavior ◽  
Qualitative Properties ◽  
Partial Differential ◽  
Nonclassical Symmetry ◽  
Symmetry Method

AbstractThe generalized conditional symmetry method is applied to study the reduction to finite-dimensional dynamical systems and construction of exact solutions for certain types of nonlinear partial differential equations which have many physically significant applications in physics and related sciences. The exact solutions of the resulting equations are derived via the compatibility of the generalized conditional symmetries and the considered equations, which reduces to solving some systems of ordinary differential equations. For some unsolvable systems of ordinary differential equations, the dynamical behavior and qualitative properties are also considered. To illustrate that the approach has wide application, the exact solutions of a number of nonlinear partial differential equations are also given. The method used in this paper also provides a symmetry group interpretation to some known results in the literature which cannot be obtained by the nonclassical symmetry method due to Bluman and Cole.

scholarly journals A FAMILY OF THE SPIRAL SOLUTIONS OF THE NONLINEAR KLEIN‐GORDON EQUATION

1998 ◽  
Vol 3 (1) ◽  
pp. 98-103
Author(s):  
V. V. Gudkov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Nonlinear Partial Differential Equations ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Klein Gordon ◽  
Klein Gordon Equation

A family of the functions, intended for a construction the exact travelling wave solutions of nonlinear partial differential equations, is given. Exact solutions of the Klein‐Gordon equation with a special potential are obtained. The behavior of complex and hypercomplex solutions of the second order is presented.

scholarly journals Exact Solutions for the Integrable Sixth-Order Drinfeld-Sokolov-Satsuma-Hirota System by the Analytical Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jalil Manafian Heris ◽  
Mehrdad Lakestani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Periodic Wave ◽  
Travelling Wave ◽  
Sixth Order ◽  
Mathematical Tool ◽  
Partial Differential ◽  
Wave Solutions

We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized (G′/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these methods, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

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