On the decomposition of the modified Kadomtsev-Petviashvili equation and explicit solutions

The (2+1)-dimensional modified Kadomtsev-Petviashvili equation is decomposed into two known (1+1)-dimensional soliton equations. A Darboux transformation of the two known (1+1)-dimensional soliton equations is derived with the help of a gauge transformation of the spectral problem. As an application, explicit solutions of the two (1+1)-dimensional soliton equations and two new explicit solutions of the (2+1)-dimensional modified Kadomtsev-Petviashvili equation are obtained. © 2000 American Institute of Physics.