Exact Solutions And Invariant Subspaces Of Two Family Of Nonlinear Equations

In this thesis, exact solutions and invariant subspaces of two family of nonlinear equations are discussed. Some exact solutions of these equations are constructed by invariant subspaces method. The thesis is organized as follows:In chapter1, the history of exact solutions to nonlinear partial differential equa-tions are described generally. We give a brief account of invariant subspace method.In chapter2, invariant subspaces of a family of third order nonlinear dispersive equations are given. Then exact solutions of some equations within this family are constructed. by invariant subspaces method. Peakon solutions, compacton solutions and blow-up. solutions of some equations are obtained.In chapter3, equations equivalent to the generalized inhomogeneous nonlinear’ diffusion equations are given by the pressure transformations and equivalent transformations related to invariant subspace method. Higher-dimensional invariant subspaces of equivalent e-quations are obtained. The generalized functional separable solutions of the general-ized inhomogeneous nonlinear diffusion equations can be constructed. Some examples are presented to illustrate the procedure.In chapter4, the research content is summarized.