The separation technique for nonlinear partial differential equations: general results and its connection with other methods

This thesis is primarily a study of the separation method for solving nonlinear partial differential equations, which is a generalisation of the classical separation approach as applied to linear equations. The method is of Importance since it produces physically useful solutions, such as travelling wave and soliton solutions, to the interesting nonlinear equations of current interest in a simple and economical way. This work is also concerned with the relationships between this method and the other standard systematic methods for solving nonlinear partial differential equations. As a start In this direction, a preliminary investigation of the correspondence of separable and similarity solutions is carried out. The thesis also uses the separation technique to study the non-solvability -of equations by 1ST assuming that the Ablowitz conjecture is true. The thesis commences with a general Introduction which includes the standard systematic methods for solving nonlinear partial differential equations. Chapters two and three deal with the properties and applications of the separation technique and extend existing results. Chapters four and five use the separation technique in the Painleve test and the final chapter concerns the connection between similarity solutions and separable solutions