Soliton solutions of Burgers' equation and the modified Kadomtsev-Petviashvili equation

摘要

From the Levi spectral problem, we obtain the (1+1)-dimensional Burgers' equation and the (2+1)-dimensional modified Kadomtsev-Petviashvili equation. Through the Miura transformation, the modified Kadomtsev-Petviashvili equation is transformed into the Kadomtsev-Petviashvili equation. Then by constructing some new Darboux transformations, we obtain new soliton solutions of Burgers' equation and find solitons fusion. By solving two (1+1)-dimensional soliton equations, new soliton solutions of the modified Kadomtsev-Petviashvili equation are obtained. And then explicit solutions of the Kadomtsev-Petviashvili equation are also obtained through the Miura transformation.