Application of lie group methods to certain partial differential equations

Thesis (Msc. in Applied Mathematics) North-West University, Mafikeng Campus, 2012In the first part of this work, two nonlinear partial differential equations, namely, a modified Camassa-Holm-Degasperis-Procesi equation and the generalized Kortewegde Vries equation with two power law nonlinearities are studied. The Lie symmetry method along with the simplest equation method is used to construct exact Solutions for these two equations. The second part looks at two systems of partial differential equations, namely, the generalized Boussinesq-Burgers equations and the (2+1)-dimensional Davey-Stewartson equations. The Lie symmetry method and the travelling wave hypothesis approach are utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the (2+ 1 )-dimensional Davey-Stewartson equations.Master