Research On Exact Solutions Of Nonlinear Partial Differential Equations

As our society develops,a multitude of nonlinear phenomena havebeen occurred．These nonlinear phenomena in many practical problems canbe described by nonlinear partial differential equations．It is an extremelyimportant and worthwhile work to find out the solutions for the nonlinearpartial differential equations．For a long term,people have done a lot ofresearch in the field．Different methods are given for solving certainnonlinear partial differential equations,and many new solutions of greatsignificance are found．A general method is presented to get a combinationhomoclinic orbit solution in this paper．We obtain some combinationhomoclinic orbit solutions of some nonlinear partial differential equations．Firstly the equations are transferred into bilinear forms by the dependentvariable transformations,the bilinear equations are solved by using theproperty for Hirota's bilinear operator．The paper consists of four chapters．Chapter one is an introduction part．Some methods to solve nonlinearpartial differential equations are given．The main results are described． Chapter two introduces Hirota's bilinear method including the origin andthe property for Hirota's bilinear operator．Then the general method to getand the combination homoclinic orbit solution are given．Chapter three presents the main results．The combination homoclinic orbitsolutions for the (2+1)-dimensional long wave-short wave interactionsolution,Mel'nikov equation and g-Schr(o|¨)dinger equation are obtained．Chapter four is summary and prospect．...