Novel Mixed Solutions Of Some Partial Differential Equations And Their Local Excitation Modes

In recent years,the research on soliton molecules has been an upsurge.In this paper,we mainly use the Hirota bilinear method and other methods to study the new mixed solutions and local excitation modes of four partial differential equations.The first chapter introduces the development and present situation of the soliton theory,and introduces some methods to study the exact solution of nonlinear partial differential property.In chapter 2,the D’Alembert wave solution of(2+1)-dimensional generalized NNV equation is obtained by traveling wave transformation,and its N=2,3,4 soliton molecules are obtained by means of velocity resonance method.In chapter 3,the local wave solutions of(2+1)-dimensional dissipative AKNS equation,including lump wave and lump-type wave,are studied by means of the proposed method,and the motion trajectories of lump wave are plotted with the help of Maple software.In chapter 4,three local wave solutions of the(2+1)-dimensional potential BLMP equation are studied and their dynamic behaviors are analyzed by using the method of variable separation.By adding new constraints,the fission and fusion solutions of(2+1)-dimensional generalized KDKK equation are obtained,and a variety of new mixed solutions are obtained.The research results are shown in chapter 5.Finally,it is the summary and prospect of the article content.