Some Exact Solutions for the Fifth-Order KdV Equation with Constant Coefficients by the Lie Symmetries
Njara Lova Razafintsalama *
Department de Physique, University of Toliara, Madagascar.
Christian Rakotonirina
Institut Supérieur de Technologie d’Antananarivo, IST-T, Madagascar.
Adolphe AndriamangaRatiarison
Laboratoire de la Dynamique de l’Atmosphère, du Climat et des Océans, DyACO, University of Antananarivo, Madagascar.
*Author to whom correspondence should be addressed.
Abstract
The importance of the nonlinear equation on which the Lie method is applied lies in its ability to solve complex problems that cannot be addressed by classical linear methods. In this work, we use the Lie symmetries to obtain particular solutions for the fifth-order Korteweg de Vries equation. Our original equation is a nonlinear partial differential evolution equation (PDEE). We convert this equation to the nonlinear ordinary differential equation by reducing the variables. We determine the solution of the initial equation by using the solution obtained via the Lie symmetry method of the nonlinear ordinary differential equation.
Keywords: Fourth-order nonlinear ordinary differential equation, characteristic variable, travelling wave, invariant solution, fifth-order korteweg de vries equation, lie symmetries