Conservation laws and solutions of the Drinfel'd-Sokolov-Wilson system, the Boussinesq system and the complex modified KdV equation

Abstract

In this dissertation the conservation laws for the Drinfel 'd-Sokolov-Wilson, modified Korteweg-de Vries and the Boussinesq system will be derived using the Noether approach. Noether approach requires the knowledge of a Lagrangian. Since these systems are of third order, they do not have a Lagrangian and therefore we will increase the order of the systems by one. The new systems obtained have Lagrangians and so Neother approach can be used to find the conservation laws. The inverse transformation will then be used to obtain the conservation laws for the underlying systems. Moreover the exact solutions of the Drinfel'd-Sokolov-Wilson and modified Kortewegde Vries systems will be obtained using the ( G' / G)-expansion method. The Lie point symmetries for the Boussii1esq system will be calculated.