Rational Soliton Solutions Of Nonlocal Coupled Nonlinear Schr(?)dinger Equations And Lump Solutions And Interactional Solutions Of(3+1)-dimensional B-type Kadomtsev-Petviashvili Equation

Soliton theory plays an important role in nonlinear science,in which soliton equation is an important part of soliton theory.The problem of solving the exact solution of soliton equation not only promotes the study of soliton theory,but also reasonably explains some nonlinear phenomena in nature.In this paper,we mainly study rational soliton solutions in the parity-time-symmetric nonlocal coupled nonlinear Schr?dinger equations,lump solutions and interaction solutions of(3+1)-dimensional generalized B-type Kadomtsev-Petviashvili(BKP)equation.Based on the obtained relevant solutions,the time development characteristics and interaction of the solutions are analyzed deeply with the help of the Mathematica software.The main research work of this paper includes the following two aspects:(1)By constructing the classical and generalized Darboux transformations,the rational soliton solutions of the nonlocal coupled nonlinear Schr?dinger equations with parity-time-symmetric are derived under the condition of non-vanishing background.In order to analyze the collision properties of solitons,we make the asymptotic expressions of first-order rational solitons,and find that there are three kinds of elastic collisions of soliton interactions of antidark-antidark,dark-antidark,and antidark-dark rational solitons.In addition,it is found that the second-order rational solution possesses abundant interaction patterns.These analytical results have potential application value for the study of nonlinear phenomena in parity-time-symmetric optical fiber system.(2)Based on the Hirota bilinear method and the limit technique of long wave,lump solutions and interaction solutions of(3+1)-dimensional BKP equation are obtained.We analyze the spatial-temporal structure and interaction behavior of lump solution and discuss the collision behavior of solitary wave and lump solution.We hope that the research methods and results of the two nonlinear equations in this paper can provide some help to the solution of other soliton equations,and also hope to explain the related mathematical and physical phenomena.