Study On The Exact Solutions Of Two Soliton Equations

At present,more and more researchers pay close attention to the solutions of soliton equations.Because these solutions can explain physical phenomena well.In this paper,based on the Hirota bilinear method and symbolic computation,the exact solutions of two soliton equations are studied.In the first part,a class of soliton,breather,lump and interaction solution of a dimensionally reduced Jimbo-Miwa-Like equation is explicitly generated.According to the Hirota bilinear method,N-soliton solutions are constructed,applying the complex conjugate method on multi-soliton solutions,breathers and related interaction solutions are obtained.Afterwards,lump and lump-kink soliton solutions are gained based on the square function method.Moreover,some graphs are given out to demonstrate the dynamic properties of the localized wave solutions.In the second part,soliton solutions,fissionable wave solutions,M-lump solutions and interaction solutions of the(4+1)-dimensional Fokas equation are explicitly generated.Taking advantage of the Hirota bilinear method,N-soliton solutions are constructed.Then,on bases of the obtained soliton solutions,fissionable wave solutions are ascertained by appropriate selections of parameters.Applying the long wave limit method and restricting the conjugation conditions on the related solitons,M-lump solutions are derived.Afterwards,the interaction solutions which describe interactions of a lump and a soliton,a lump and two solitons,a lump and fifissionable solitary waves are gained.Moreover,some graphs are given out to demonstrate the dynamic properties of the explicit analytical localized wave solutions.