Generalized Separation Of Variables For Solving Exact Solutions Of Nonlinear Evolution Equations

In this dissertation, by applying the ideas of generalized separation of variables pro-posed by Titov and Galaktionov and Wu's method proposed by famous mathematicianWu Wentsun, we considers the calculation of exact solutions to nonlinear evolution arisingfrom the field of mechanics and physics and the algorithm is implemented in symboliccomputation software Mathematica.In chapter 1, as a preparative knowledge, the main results about symmetry theoryand Wu's method are introduced, in addition some fundamental definitions, such as trans-formation group, infinitesimal operator, prolongation, first integral, infinitesimal criterionfbr invariance of an ODE, characteristic set are recalled.In chapter 2, as the main result obtained in this paper, a generalized algorithm ofseparation variables is given and as an application of the method, some two and three-order nonlinear evolution equations are solved and some new and general solutions areobtained. Consequently the form of the equations suited to the algorithm is extended.In chapter 3, the problems of constructing finite-dimensional functional linear invari-ant spaces under a given differential operator as well as an inverse problem concerning thedescription of all operators possessing a given invariant space are investigated.In chapter 4, the original code of implemented program and the operating instructionare given.In chapter 5, a conclusion remark and many new tasks are presented.