The lie symmetry analysis of third order Korteweg-de Vries equation

Abstract

This study sought to analyse the Lie symmetry of third order Korteweg-de Vries equation. Solving nonlinear partial differential equations is of great importance in the world of dynamics. Korteweg-de Vries equations are partial differential equations arising from the theory of long waves, modelling of shallow water waves, fluid mechanics, plasma fluids and many other nonlinear physical systems, and their effects are relevant in real life. In this study, Lie symmetry analysis is demonstrated in finding the symmetry solutions of the third-order KdV equation of the form. The study systematically showed the formula to find the specific solution attained by developing prolongations, infinitesimal transformations and generators, adjoint symmetries, variation symmetries, invariant transformation and integrating factors to obtain all the lie groups presented by the equation. In conclusion, infinitesimal generators, group transformations and symmetry solutions of third-order KdV equation are acquired using a method of Lie symmetry analysis. This was achieved by generating infinitesimal generators which act on the KdV equation to form infinitesimal transformations. It can be seen from the solutions of this paper that the Lie symmetry analysis method is an effective and best mathematical technique for studying linear and nonlinear PDEs and ODEs.