2N line-soliton solutions of the (2+1)-dimensional Kadomtsev-Petviashvili equation can be presented by resorting to the Hirota bilinear method. By extending the real parameters into complex parameters, this paper obtains N periodic-soliton solutions of the (2+1)-dimensional Kadomtsev-Petviashvili equation from the 2N line-soliton solutions.
A new coupled integrable dispersionless equation is presented by considering a spectral problem.A Darboux transformation for the resulting coupled integrable dispersionless equation is constructed with the help of spectral problems.As an application,the N-soliton solution of the coupled integrable dispersionless equation is explicitly given.
Recently the(G'/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations.This paper shows that the(G'/G)-expansion method is a special form of the truncated Painlev'e expansion method by introducing an intermediate expansion method.Then the generalized(G'/G)-(G/G') expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev'e expansion.The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the(G'/G)-expansion method.
