Bell Polynomial Solutions Of Soliton Equations

In this thesis, we introduce Bell polynomials and Binary Bell polynomials. We also discuss the multidimensional generalization of the binary Bell polynomials. We firstly present the connection between Bell polynomials, binary Bell polynomials and Hirota D-operatoers. Since Bell polynomials can play an important role in the char-acterization of bilinearizable equations, we have a systematic approach to find Hirota bilinear form and soliton solution of soliton equations based on Bell polynomials. By choosing the binary Bell polynomial constrain(y-constrain), we can present the in-variance condition in binary Bell polynomials, then we further obtain the bilinear auto Backlund transformation and Lax Pair.