Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation

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.

[1]  Wen-Xiu Ma,et al.  A hierarchy of coupled Burgers systems possessing a hereditary structure , 1993 .

[2]  How to construct the discrete symmetries of partial differential equations , 2000, European Journal of Applied Mathematics.

[3]  Mehdi Nadjafikhah.  Lie Symmetries of Inviscid Burgers’ Equation , 2009 .

[4]  Chaudry Masood Khalique,et al.  Lie group classification and invariant solutions of mKdV equation with time-dependent coefficients , 2011 .

[5]  Liang Gao,et al.  A Note on Exact Solutions to Linear Differential Equations by the Matrix Exponential , 2009 .

[6]  Igor Leite Freire.  Note on Lie Point Symmetries of Burgers Equations , 2010 .

[7]  Min Chen,et al.  Direct search for exact solutions to the nonlinear Schrödinger equation , 2009, Appl. Math. Comput..

[8]  A. Jamiołkowski.  Book reviewApplications of Lie groups to differential equations : Peter J. Olver (School of Mathematics, University of Minnesota, Minneapolis, U.S.A): Graduate Texts in Mathematics, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1986, XXVI+497pp. , 1989 .

[9]  Min Chen,et al.  Do symmetry constraints yield exact solutions , 2007 .

[10]  George E. P. Box,et al.  The Royal Society of London , 2013 .

[11]  Zixiang Zhou,et al.  Coupled Integrable Systems Associated with a Polynomial Spectral Problem and Their Virasoro Symmetry Algebras , 1996, solv-int/9607003.

[12]  P. Hydon.  Discrete point symmetries of ordinary differential equations , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[13]  Boxi Wu,et al.  On permutation symmetries of hopfield model neural network , 2001 .

[14]  On the Lie point symmetry analysis and solutions of the inviscid Burgers equation , 2011 .

[15]  W. Miller,et al.  Group analysis of differential equations , 1982 .

[16]  Classification of Similarity Solutions for Inviscid Burgers’ Equation , 2010 .

[17]  Maria Luz Gandarias,et al.  Classical and Nonclassical Symmetries of a Generalized Boussinesq Equation , 1998 .

[18]  Mehdi Nadjafikhah,et al.  Symmetry group classification for general Burgers’ equation , 2009, Communications in Nonlinear Science and Numerical Simulation.

[19]  S. Lie,et al.  Vorlesungen über Differentialgleichungen, mit bekannten infinitesimalen Transformationen , 1891 .

[20]  G. Bluman,et al.  Symmetries and differential equations , 1989 .