B(a|¨)cklund Transformation And Superposition Formula For Solutions Of Nonlinear Equations

In this dissertation, with the help of Hirota bilinear transformation methodand Painlevé analysis we studied some nonlinear partial differential equationsand the bilinear derivative equations，the multiple soliton solutions，theB cklund transformations，the superposition formulas for solutions and theverification of the Painlevé property of these equations are presented. Themain results are as follows:1. A short introduction for the concept of bilinear differential operator withits basic properties and the derivation of bilinear derivative equations aregiven.2. The Hirota bilinear transformation method is used to construct thebilinear derivative equations，the multiple soliton solutions，the B cklundtransformations，the superposition formulas for solutions of two kinds ofextended KP equations.3.The Hirota bilinear transformation method and Riemann theta functionare used to construct the periodic wave solution of the Sawada-Koteraequation. The soliton solutions are obtained via an appropriate limitprocedure.4. The WTC approach of Painlevé analysis is used to verify the Painlevéproperty of a system of partial differential equations and its B cklund transformation is also presented.