Study On Soliton Of Some Non - Isospectral Integrable Equations

In this thesis, we mainly consider some properties of nonisospectral integrableequations, and use the Hirota method and Wronskian technique to solve soliton solutions forthese equations. Soliton resonance properties of soliton are illustrated, and dynamicalproperties of soliton are discussed in inhomogeneous media. In the first chapter, weintroduce the development of soliton theory, as well as the current research situation, and theanalytic solving way of the nonisospectral equations. In the second chapter, the solitoninteraction is investigated based on solving the nonisospectral generalizedSawada–Kotera(GSK) equation. By using Hirota method, the analytic one-, two-, three-andN-soliton solutions of this model are obtained. According to those solutions, the relevantproperties and features of soliton are illustrated. The results of this chapter will be importantto the study of soliton resonance in the inhomogeneous media. In the third chapter, thebilinear form of the nonisospectral generalized Sawada–Kotera equation is derived. With theaid of the Wronskian technique, the Wronskian solution is presented for this equation.Negatons and positons are obtained, and the dynamical properties of these solutions arediscussed by2D figures and density figures. Soliton resonance is also discussed in theinhomogeneous media. In the fourth chapter, double Wronskian conditions for thenonisospectral BKP equation are derived. The soliton solutions in double Wronskian formare given. Soliton properties for two-soliton are discussed by3D figures and density figures.In the fifth chapter, we summarize the thesis, and prospect the future work.