A Study Of Some Exact Solutions Of (2+1)-Dimensional BLMP Equation And Their Dynamical Behaviors

The solution of nonlinear equations can not only describe many natural phenomena and dynamical behaviors,reveal the changing rules of things,but also provide theoretical reference for many application problems.Therefore,the research on the solution of nonlinear equations is very important in nonlinear science,and it is a hot and frontier topic in the world.The(2 + 1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation is an important integrable model in nonlinear science.It is widely used in fluid,plasma,traffic flow,nanomaterials and other fields of physical and chemical engineering.In this thesis,based on the symbolic computing software Maple and numerical technology,we study several kinds of exact solutions of the BLMP equation and discuss their dynamical behaviors via numerical figures.The detailed research contents are as follows.1)By introducing a special transformation and using the Hirota bilinear method,we construct the N-soliton solutions of the BLMP equation.Then,by applying the long wave limit method and complex conjugate constraint to the corresponding N-soliton solutions,abundant nonlinear local wave solutions are obtained,including 2-breathers,2-lumps,four kinds of interaction solutions composed of single(double)soliton(s)and lump / breather,and mixed solutions composed of single soliton and 2-breather,2-lump,1-lump and 1-breather.Finally,we study the dynamical behaviors of these solutions via numerical simulations.2)By using the mechanism of velocity resonance and mode resonance,we obtain abundant breather molecules,breather-soliton molecules and their interaction mixed solutions of the BLMP equation,which include the mixed solutions composed of breather-soliton molecule and single soliton / double soliton / breather,the mixed solutions composed of breathing molecule and single soliton,and the mixed solutions composed of two different breather-soliton molecules.By choosing appropriate parameters,the dynamical behaviors of these solutions are studied.The two kinds of solutions of BLMP equation obtained in this paper are completely new;Moreover,our method of constructing these two kinds of solutions is also brand-new.It has generality,that is,it can be effectively used to construct higher-order lumps,breathers,breather molecules,breather-soliton molecules and their interaction solutions for other nonlinear differential equations.These results can provide some theoretical references for experts in related fields to study the propagation characteristics of nonlinear waves.