Lie Group Applications to Some Nonlinear Systems

Abstract

In this thesis, we study the applications of Lie group theory to the nonlinear partial differential equations (PDEs) or their systems which represent some of the important physical phenomena. Our primary objective in this thesis is to identify the symmetries of PDEs in order to obtain exact solutions and a further point is also to discuss the integrability and physical behaviour of the equations. The investigations carried out in this thesis are confined to the applications of Lie group methods to the six nonlinear systems which are the (2+1)-dimensional Calogero Degasperis (CD) equation with its generalized form, the coupled Klein-Gordon-Schr¨odinger (KGS) equation along its variable coefficients form, the (2+1)-dimensional potential Kadomstev Petviashvili (PKP) equation and its generalized form, the generalize Dullin-Gottwald-Holm (GDGH) equation and the generalized Bretherton equation.