The Novel Multisoliton Solutions For Some Soliton Equations

In this paper, we consider the solution of some soliton equations by Hirota method, Wronskian technique and B(?)cklund transformation. The novel multisoliton solutions for the KP equation, the nonlinear lumped self-dual network equations, the Toda lattice and the nonlinear Schr(?)dinger equation are derived by using of Hirota direct method. The KP equation and the Toda lattice have also solutions in new Wronskian form . In addition, taking the KP equation as example we also show the novel solutions obtained by Backlund transformation are coincidence with the novel solution obtained through Hirota method. The above three methods are easily to be extended to some other soliton equations.The paper also proposes a KP equation with self-consistent sources from the linear problem of the KP system. One-, two- and even three-soliton solutions are successively constructed through the standard Hirota's approach. On the basis of this, We conjecture further a general formula of N-soliton solution. We also use Wronskian technique to give Wronski determinant solutions. By virtue of some determinantal identities, solution is verified by direct substitution into the bilinear equations of the KP equation with self-consistent sources. The coincidence of the N-soliton solutions obtained by Hirota method and Wronskian technique is proved. The novel multisoliton solutions for the KP equation with self-consistent sources are also obtained by Hirota method.Apart from that, the bilinear equation and bilinear B(?)cklund transformation for the nonisospectral KP equation and the nonisospectral KdV equation are obtained. Exact solutions are constructed in terms of Wronskian and are verified by direct substitution to the satisfy the bilinear equation and the assiciated B(?)cklund transofrmation respectively. These two nonisospectral equations are also solved through the Hirota method. Finally, some figures are presented to show the shape and motion of the soliton solutions for some equations.