The Wronskian Solutions Of Nolinear Partial Differential Equations

The soliton theory is an important constituent part of applied mathematics and mathematical physics, it has been caught close attention in the domain of international mathematics and physics for a decade, and one of the important things is to seek the method of solving the soliton equations. Seeking the exact solutions of soliton equations not only helps us understand the nature and algebraic structure further, but also give us a reasonable explanation of the related natural phenomenon. In this paper, we focus on soliton solutions of three kinds of partial differential equations with different dimensions by Wronskian technique, which includes the following aspects:First, we change the classical Boussinesq equation into a member of AKNS hierarchy by equivalent transformation, and get multisoliton solutions of AKNS equation by means of constructing the double Wronskian deteminant matrix, and then we can get the corresponding multisoliton solutions of the Boussinesq equation.Second, we get the bilinear form of (2+1)-dimensinal bSK equation with the the bilinear transformation. Then, choose the proper functionφj, and contribute the Wronskian determinant solutions. Finally substitude the Wronskian determinant solutions into the bilinear equations, and verify the solutions are correct.Third, apply the bilinear transformation to the (3+1)-dimensinal Boussinesq equation, and get the bilinear form, then use the Wronskian technique to get the expressions of single soliton solution, double soliton solution and N-soliton solution.