The N-soliton Solution And Soliton Molecules For Several Partial Differential Equations

In this paper,the N-soliton solution and soliton molecules of some partial differ-ential equations are discussed.Based on the Hirota's bilinear method,the N-soliton solution of partial differential equation is solved,and the phenomenon of soliton reso-nance is also analyzed.Then,the method of velocity resonance and module resonance are used to solve soliton molecules problem of partial differential equations.In the first chapter,the development and present situation of the soliton,the solving method of the nonlinear partial differential equation and the main work of this paper are introduced.In chapter 2,the(3+1)-dimension potential-Yu-Toda-Sasa-Fukuyama(YTSF)equation is reduced by variable substitution,and potential-YTSF equation's bilinear equation is derived by Hirota's bilinear method.By selecting special constraints,the equations for breathe soliton,lump soliton and their interactive solutions can be obtained.In chapter 3 and 4,based on the N soliton solutions,velocity resonance and module res-onance conditions are used to study the soliton molecules of the(2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation and the isospec-tral BKP equation.Finally,the image of partial differential equation solution is drawn by computer software,and the image is analyzed.In chapter 5,makes the summary and the prospect to the article.