On adjoint symmetries and reciprocal Bäcklund transformations of evolution equations

Abstract: The aim of this Licentiate Thesis is to discuss special transformations and so-called adjoint symmetries of nonlinear partial differential equations. Nonlinear partial differential equations play an important role in the  description of many physical phenomena. In order to understand the phenomena, modelled by the equations mentioned above, it is therefore necessary to obtain and analyze the solutions and the conservation laws of these equations. In this Thesis we investigate some methods to obtain conservation laws and transformations between nonlinear partial differential equations  and moreover to classify nonlinear partial differential equations with respect to those methods. The main emphasis is on adjoint symmetries and transformations of  evolution equations. In particular we study the adjoint symmetries and the construction of reciprocal Bäcklund transformations for evolution equations.