Lie symmetry solutions of sawada- kotera equation

Abstract

The problems of di erential equations are encountered in physical elds, engi- neering elds and mathematical world thus it is so important to nd their exact solutions.The exact solutions of partial di erential equations and ordinary di er- ential equations have been sought by scholars for a number of decades. Researchers have used Lie symmetry approach to solve ordinary di erential equations and par- tial di erential equations. The progressive wave solution of one-dimensional wave equation was rst discovered by Jeane Le Rond D' Atemmbert (1717-1783).His solution was a special application of the method of characteristics. The Sawada- Kotera equation is a special form of wave equation and the generalized Riccati equation mapping with the essential quotient group expansion techniques on con- structing plentiful traveling wave results has been used in the past to solve the Sawada-Kotera equation among many other methods but the results the were not easily found since one could make errors during the plotting of graphs. In this study, we concentrated on analysis of fth order Sawada-Kotera equation of the form; ut + 45u2ux + 15uxuxx + 15uuxxx + uxxxxx = 0 using Lie symmetry analysis because the solution does not depend on the initial and boundary values hence is not an approximation to the exact solution and it has not been solved previously using this method. The study aimed at obtaining all the Lie groups admitted by the equation, invariant and exact solutions and symmetry solutions. The method- ology involved application of in nitesimal transformations and generators, prolon- gations, adjoint symmetries, variation symmetries, invariant transformation and integrating factors so as to establish all the Lie groups shown by the equation.Our obtained solutions demonstrated that Lie symmetry analysis method is a sraight forward and best mathematical tool used to obtain analytical solutions of highly nonlinear PDEs.