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.

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 How to construct the discrete symmetries of partial differential equations

2000 ◽  
Vol 11 (5) ◽  
pp. 515-527 ◽  
Author(s):  
P. E. HYDON
Keyword(s):  
Differential Equation ◽  
Discrete Symmetries ◽  
Gas Dynamics ◽  
Burgers Equation ◽  
Lie Point Symmetries ◽  
Discrete Point ◽  
Nonlocal Symmetry ◽  
Partial Differential ◽  
Nontrivial Group ◽  
Harry Dym Equation

This paper introduces an algorithm for calculating all discrete point symmetries of a given partial differential equation with a known nontrivial group of Lie point symmetries. The method enables the user to determine the discrete symmetries with little more effort than is used to find the Lie symmetries. It is used to obtain the discrete point symmetries of Burgers' equation, the spherical Burgers' equation, and the Harry–Dym equation. The method can be extended to some types of nonlocal symmetry; we derive the quasi-local discrete symmetries of a system of PDEs from gas dynamics.

Symmetry operators and exact solutions of a type of time-fractional Burgers–KdV equation

2019 ◽  
Vol 16 (02) ◽  
pp. 1950032 ◽  
Author(s):  
Azadeh Naderifard ◽  
S. Reza Hejazi ◽  
Elham Dastranj ◽  
Ahmad Motamednezhad
Keyword(s):  
Exact Solutions ◽  
Fourth Order ◽  
Vector Fields ◽  
Kdv Equation ◽  
Group Analysis ◽  
Invariant Subspaces ◽  
Similarity Solutions ◽  
Optimal System ◽  
Lie Point Symmetries ◽  
Symmetry Operators

In this paper, group analysis of the fourth-order time-fractional Burgers–Korteweg–de Vries (KdV) equation is considered. Geometric vector fields of Lie point symmetries of the equation are investigated and the corresponding optimal system is found. Similarity solutions of the equation are presented by using the obtained optimal system. Finally, a useful method called invariant subspaces is applied in order to find another solutions.

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