Constructing Exact Solutions Of A Class Of Nonlinear Evolution Equations

Soliton theory has always played a pivotal role in the fields of applied mathematics and mathematical physics.In particular,the question of seeking the soliton solution of the equation is one of the most popular studies.At present,many scholars have done a series of research on their solution methods.Based on the nonlinear evolution equa-tions,this paper discusses several methods for constructing exact solutions of nonlinear evolution equations and methods for constructing their conservation laws.The details are as follows:First part.It describes the research background and main research contents of this paper,and gives a brief introduction to some typical mathematical physics methods that will be used.Second part.Two forms of soliton solutions of Boussinesq equation are con-structed by two different methods.Third part.Based on the general Hirota bilinear form,the numerical solution of the(2+1)-dimensional B-type Kadomtsev Petviashvili equation is first studied.Some constraints are found to guarantee the enthusiasm and locality of the block solution.We also analyze the amplitude,motion direction and horizontal velocity of the clonic soliton wave,and effectively explain more phenomena in fluid or plasma mechanics.Secondly,we give the compound solution of the(2+1)-dimensional Konopelchenko-Dubrovsky equation.Fourth part.In the sense of Caputo and Riemann-Liouville fractional derivatives,the Bogoyavlenskii KdV coupled system is simplified to a special system of fractional ordinary differential equations by Lie symmetric analysis,and this simplified system is defined in the sense of Erdelyi Kober(EK).Therefore,we also give the power series solution of the original equation.Finally,using the new conservation theory and the extension of the Noether operator,the non-local conservation law of Bogoyavlenskii KdV coupled system is constructed.Fifth part.Some important contents of this paper and the prospects for future work were disscussed.