Analytical Study Of Nonlinear Models

The discovery of optical solitons and breathers in fiber-optic com-munication has promoted the development of communication technology.Mathematical models in fluid mechanics and optical field have helped the scientists predict and solved practical problems.The development of nonlinear science has made the theory and practice more closely con-nected.More and more nonlinear models have been proposed to simulate nonlinear phenomena in our daily life.The main work of this paper is to systematically analyze three types of nonlinear models:a class of constant coefficient partial differential equations,a class of constant variable partial differential equations,and a class of variable coefficient(function)partial differential equations,and to solve and analyze the relevant properties of some waves.The main content of this article is as follows:(1)Analyze the(3+1)-dimensional B-type Kadomtsev-Petviashvili-Boussinesq(BKPB)equation with constant coefficients.Solve the lump solutions,breather-type kink soliton solutions,rogue-wave solutions and semi-rational solutions of BKPB equation;The linear rogue-wave in spe-cial form is derived from the obtained lump solutions;Study the interac-tion between soliton,rogue-wave and lump wave.(2)Analyze the(3+1)Kudryashov-Sinelshchikov equation with con-stant variable coefficients.The Backlund transform and lump solutions of the equation are obtained,and the motion path of the lump on the two-dimensional plane is obtained.The effect of the constant variable coefficients on the motion path of the lumps is analyzed.Based on lump solutions,a class of semi-rational solutions is derived,and take special coefficient values to analyze the two types of phenomena where the lump is cut off by the soliton.(3)Analyze a type of(3+1)dimensional shallow water-wave equa-tions with variable coefficients,where the coefficients are the functions of t,and set a type of rational and semi-rational solutions of this equa-tion,which is different from those in equations with constant variable coefficients.Describe and analyze the interaction of soliton,lump and rogue-wave based on the semi-rational solutions,and focus on analyzing the influence of the variable coefficients on waves.