Exact Solutions of the General Variable Coefficient Kdv-Burgers Equation

2020 ◽  
Vol 09 (03) ◽  
pp. 277-284
Author(s):  
萍 张
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Burgers Equation

scholarly journals Improved hyperbolic function method and exact solutions for variable coefficient Benjamin-Bona-Mahony-Burgers equation

2015 ◽  
Vol 19 (4) ◽  
pp. 1183-1187
Author(s):  
Hong-Cai Ma ◽  
Xiao-Fang Peng ◽  
Dan-Dan Yao
Keyword(s):  
Fluid Mechanics ◽  
Exact Solutions ◽  
Variable Coefficient ◽  
Function Method ◽  
Burgers Equation ◽  
Periodic Wave ◽  
Hyperbolic Function ◽  
Hyperbolic Function Method

By using the improved hyperbolic function method, we investigate the variable coefficient Benjamin-Bona-Mahony-Burgers equation which is very important in fluid mechanics. Some exact solutions are obtained. Under some conditions, the periodic wave leads to the kink-like wave.

scholarly journals Symmetry Classification and Exact Solutions of a Variable Coefficient Space-Time Fractional Potential Burgers’ Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Manoj Gaur ◽  
K. Singh
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Burgers Equation ◽  
Space Time ◽  
Subspace Method ◽  
Group Invariant ◽  
Infinitesimal Generators ◽  
Symmetry Properties ◽  
Coefficient Space ◽  
Group Invariant Solutions

We investigate the symmetry properties of a variable coefficient space-time fractional potential Burgers’ equation. Fractional Lie symmetries and corresponding infinitesimal generators are obtained. With the help of the infinitesimal generators, some group invariant solutions are deduced. Further, some exact solutions of fractional potential Burgers’ equation are generated by the invariant subspace method.

SOLVING THE GENERALIZED BURGERS–KdV EQUATION BY A COMBINATION METHOD

2008 ◽  
Vol 22 (21) ◽  
pp. 2021-2025 ◽  
Author(s):  
YUANXI XIE
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Combination Method ◽  
Generalized Kdv Equation ◽  
Generalized Burgers Equation

In view of the analysis on the characteristics of the generalized Burgers equation, generalized KdV equation and generalized Burgers–KdV equation, a combination method is presented to seek the explicit and exact solutions to the generalized Burgers–KdV equation by combining with those of the generalized Burgers equation and generalized KdV equation. As a result, many explicit and exact solutions for the generalized Burgers–KdV equation are successfully obtained by this technique.

scholarly journals Generalized Kudryashov Method for Time-Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Yusuf Pandir ◽  
Hasan Bulut
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Third Order ◽  
Hilliard Equation ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Cahn Hilliard Equation

In this study, the generalized Kudryashov method (GKM) is handled to find exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. These time-fractional equations can be turned into another nonlinear ordinary differantial equation by travelling wave transformation. Then, GKM has been implemented to attain exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. Also, some new hyperbolic function solutions have been obtained by using this method. It can be said that this method is a generalized form of the classical Kudryashov method.

scholarly journals Complex PT -symmetric nonlinear Schrödinger equation and Burgers equation

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120059 ◽  
Author(s):  
Zhenya Yan
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Wave ◽  
Schrodinger Equation ◽  
Wave Equations ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Wave Equations ◽  
Nonlinear Schrödinger

The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg–de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schrödinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report on exact solutions of one- and two-dimensional nonlinear Schrödinger equations (known as the Gross–Pitaevskii equation in Bose–Einstein condensates) with several complex -symmetric potentials. Finally, some complex -symmetric extension principles are used to generate some complex -symmetric nonlinear wave equations starting from both -symmetric (e.g. the KdV equation) and non- -symmetric (e.g. the Burgers equation) nonlinear wave equations. In particular, we discuss exact solutions of some representative ones of the complex -symmetric Burgers equation in detail.

Sign in / Sign up

Export Citation Format

Share Document