Exact Solutions For Nonlinear Evolution Equations With Nonlinear Terms Of Any Order

Finding the exact solution of nonlinear evolution equations is one of the most important topics in mathematical and physical fields. Some interested results are given in this thesis, such as: the high-order subsidiary equation method is used to explore the exact solution of the variable coefficient nonlinear evolution equations and the stochastic nonlinear evolution equations .This thesis is organized as follows.In chapter 1, the nonlinear evolution equation and exact solution are introduced, the history and development of the nonlinear evolution equations with nonlinear terms of any order are reviewed, and primary contents are reported as well.In chapter 2, the high-order subsidiary ordinary differential equation (sub-ODE) method is introduced , two types high-order subsidiary ordinary differential equations and their solutions are listed.In chapter 3, with the aids of the two types high-order subsidiary ordinary differential equations which ware proposed in chapter 2, the solutions of the generalized Hamilton amplitude equation with a high-order nonlinear term and the generalized Davey-Stewartson equations with nonlinear terms of any orders are derived.In chapter 4, the high-order subsidiary ordinary differential equation method is used to study the variable coefficient nonlinear evolution equations, the exact solutions (including the kink type solitary wave, the bell type solitary wave, the algebraic solitary wave and the sinusoidal traveling wave) for a variable coefficient generalized long–short wave resonance equation with nonlinear terms of any order are derived.In chapter 5, the wick-type NLS equations are generalized, the exact solutions (including the kink type solitary wave, the bell type solitary wave, the algebraic solitary wave and the sinusoidal traveling wave) for the generalized wick-type stochastic NLS equations with nonlinear terms of any order are derived.In chapter 6, the major conclusions of this thesis are listed, and the future development of the exact solution for nonlinear evolution equations is presented.