Classic Bb Equation And Generalized Wki Equation Darboux Transformation And Soliton Solutions

We focus on the Darboux transformations and soliton solutions for classical BB and generalized WKI equations respectively in this thesis, which includes the following three chapters.In chapter 1, we briefly recall the origination and development of the soliton theory, especially the research status of the Darboux transformation.In chapter 2, Based on its Lax pair, two basic Darboux transformations for the classical BB equation are established. These Darboux transformations are further applied in obtaining new soliton solutions of the classical BB equation.In chapter 3, a systematic method is proposed to construct the Darboux transformation for a generalized WKI equation. New soliton-like solutions for the generalized WKI equation are obtained by using its Darboux transformation.