Group Theoretic Techniques and Their Applications to Some Nonlinear Systems

Abstract

The objective of this thesis is to exploit the group theorectic techniques for solving nonlinear partial di fferential equations (PDEs). Main aim of the present work is to nd the symmetries of nonlinear PDEs in order to obtain their exact solutions by using di erent methods. Five nonlinear systems viz. generalized Kuramoto Sivashinsky equation, generalized Gardner equation, Benny equation, extended Ostrovsky equation and Gowdy equations are investigated for the symmetries and their solutions. Benny equation and extended Ostrovsky equation are also checked for their integrability by Painlev e test.