AUTHOR=Guo Baoyong 

TITLE=Lax integrability and soliton solutions of the (2 + 1)- dimensional Kadomtsev– Petviashvili– Sawada–Kotera– Ramani equation

JOURNAL=Frontiers in Physics

VOLUME=Volume 10 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.1067405

DOI=10.3389/fphy.2022.1067405

ISSN=2296-424X

ABSTRACT=In this paper, a new (2+1)-dimensional nonlinear evolution equation is investigated. This equation is called Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation, which can be seen as the two-dimensional extension of the Korteweg-de Vries-Sawada-Kotera-Ramani equation. By means of the Hirota's bilinear operator and the binary Bell polynomials, the bilinear form and the bilinear B\"acklund transformation are obtained. Furthermore, by application of the Hopf-Cole transformation, the Lax pair is also derived. By introducing the new potential function, the infinitely many conservation laws are constructed. Therefore, the Lax integrability of the equation is revealed for the first time. Finally, as the analytical solutions, the $N$-soliton solutions are presented.