Exact Solution Of Soliton Equations And Its Symbolic Computation Research

In this paper, with the help of symbol computation, we consider the solutions of some soliton equations by Hirota method, bilinear Backlund transformation, Wronskian and Pfaffian technique. It is evident that Hirota bilinear method is a powerful tool for solving a wide class of nonlinear evolution equation. More remarkable is that various physically important solutions to the soliton equations can be presented explicitly by means of Hirota bilinear method.In Chap 1, the Hirota bilinear method is generalized and investigated, where the Nsoliton-like solutions with singular slowly decaying at infinity for the Ramani equation is obtained. Furthermore, we also investigated the bidirectional soliton solution interaction and find singularity.In Chap 2 and 4, we consider the Boussinesq and the complex KdV equations by Hirota method, bilinear Backlund transfromation and Wronskian technique.In Chap 3, Two types of Grammian determinant solutions to the nonisospectral modified Kadomtsev-Peviashvili(mKP) equation are derived with the help of the Pfaffian derivative formulae. It should be noted that both Grammian solutions have their different characteristic.Classification Code:...