New Exact Solutions to Variable Coefficient KP Equation

2012 ◽  
Vol 166-169 ◽  
pp. 3075-3078 ◽  
Author(s):  
Jun Yi Yin
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Function Method ◽  
Group Method ◽  
Kp Equation ◽  
Group Invariant ◽  
Lie Group Method ◽  
New Exact Solutions ◽  
Solitonic Solution ◽  
Group Invariant Solutions

Two kinds of new exact solutions were offered after studying the variable coefficient KP equation, of which, the group invariant solutions of KP equation was obtained by using Lie group method, while the solitonic solution of KP equation was obtained by using hyperbola function method.

scholarly journals Invariant Solutions and Nonlinear Self-Adjointness of the Two-Component Chaplygin Gas Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Ben Gao ◽  
Yanxia Wang
Keyword(s):  
Chaplygin Gas ◽  
Group Method ◽  
Invariant Solutions ◽  
One Dimensional ◽  
Group Invariant ◽  
Lie Group Method ◽  
Two Component ◽  
Present Universe ◽  
Group Invariant Solutions ◽  
Similarity Reductions

In this paper, the Lie group method is performed on a special dark fluid, the Chaplygin gas, which describes both dark matter and dark energy in the present universe. Based on an optimal system of one-dimensional subalgebras, similarity reductions and group invariant solutions are given. Finally, by means of Ibragimov’s method, conservation laws are obtained.

scholarly journals Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax Pairs

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Na Lv ◽  
Xuegang Yuan ◽  
Jinzhi Wang
Keyword(s):  
Direct Method ◽  
Lax Pair ◽  
Group Method ◽  
Symmetry Groups ◽  
Invariant Solutions ◽  
Lax Pairs ◽  
Group Invariant ◽  
Lie Group Method ◽  
Group Invariant Solutions ◽  
Symmetry Transformations

With the aid of symbolic computation, we obtain the symmetry transformations of the (2 + 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation by Lou’s direct method which is based on Lax pairs. Moreover, we use the classical Lie group method to seek the symmetry groups of both the CDGKS equation and its Lax pair and then reduce them by the obtained symmetries. In particular, we consider the reductions of the Lax pair completely. As a result, three reduced (1 + 1)-dimensional equations with their new Lax pairs are presented and some group-invariant solutions of the equation are given.

Symmetry reduction, exact solutions and conservation laws of the Bogoyavlenskii equation

2019 ◽  
Vol 35 (01) ◽  
pp. 1950339
Author(s):  
Zhenli Wang ◽  
Chuan Zhong Li ◽  
Lihua Zhang
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Hyperbolic Function ◽  
Group Invariant ◽  
New Exact Solutions ◽  
Power Series Solutions ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions ◽  
Group Invariant Solutions ◽  
Symmetry Method

In this paper, by applying the direct symmetry method, we obtain the symmetry reductions, group invariant solutions and some new exact solutions of the Bogoyavlenskii equation, which include hyperbolic function solutions, trigonometric function solutions and power series solutions. We also give the conservation laws of the Bogoyavlenskii equation.

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.

scholarly journals Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hongwei Yang ◽  
Yunlong Shi ◽  
Baoshu Yin ◽  
Huanhe Dong
Keyword(s):  
Exact Solutions ◽  
Discrete Symmetries ◽  
Burgers Equation ◽  
Similarity Solutions ◽  
Group Method ◽  
Lie Point Symmetries ◽  
Lie Group Method ◽  
New Exact Solutions ◽  
Inviscid Burgers Equation ◽  
Infinitesimal Transformations

We discuss the Lie point symmetries and discrete symmetries of the inviscid Burgers equation. By employing the Lie group method of infinitesimal transformations, symmetry reductions and similarity solutions of the governing equation are given. Based on discrete symmetries analysis, two groups of discrete symmetries are obtained, which lead to new exact solutions of the inviscid Burgers equation.

Analytic study of solutions for a two-component Novikov system

2020 ◽  
pp. 2150025
Author(s):  
Hui Gao ◽  
Gangwei Wang
Keyword(s):  
Exact Solutions ◽  
Stationary Solutions ◽  
Invariant Solutions ◽  
Group Invariant ◽  
New Exact Solutions ◽  
Two Component ◽  
Group Invariant Solutions ◽  
Symmetry Transformations ◽  
Symmetry Method ◽  
Similarity Reductions

Under investigation in this paper is a two-component Novikov system (also called Geng-Xue equation), which was proposed by Geng and Xue in 2009. Firstly, via the Lie symmetry method, infinitesimal generators, commutator table of Lie algebra and symmetry groups of the two-component Novikov system are presented. At the same time, some group invariant solutions are computed through similarity reductions. In particular, we construct peakon solution by applying the distribution theory. In addition, based on obtained group invariant solutions and symmetry transformations, we derive some new exact solutions, which include stationary solutions, smooth solutions, and a weak solution. The analytical properties to some of group invariant solutions and new exact solutions are discussed, such as decay, asymptotic behavior, and boundedness.

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