Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Journal of Physics A: Mathematical and Theoretical
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.