Backlund Transformation And Exact Solutions For The Variable-coefficient Soliton Equations

In this thesis, based on the Hirota bilinear method, we mainly discuss three variable-coefficient equations. In chapter 1, the concept of solitons, the significance of studying soliton theory and the methods for obtaining exact solutions in soliton theory are intro-duced. In the meantime, the main work of this dissertation is also briefly introduced. In chapter 2. First of all, we find a bilinear Backlund transformation for a variable-coefficient BKP equation. Secondly, we discuss the Gramm-type pfaffian solutions for the variable-coefficient equation. Finally, we investigate the Gramm-typepfaffian solutions of a modified variable-coefficient BKP equation. Analogously, we discuss a variable-coefficient CDGKS equation in chapter 3. Chapter 4 is mainly focused on the applications of the wronskian technique in variable-coefficient equation. In this chapter, solution to a variable-coefficient BLMP equation and its Backlund transformation are also expressed by the Wronski-type determinant.