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

Abstract

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In this paper, a new (2 + 1)-dimensional nonlinear evolution equation is investigated. This equation is called the 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 Hirota’s bilinear operator and the binary Bell polynomials, the bilinear form and the bilinear Bäcklund transformation are obtained. Furthermore, by application of the Hopf-Cole transformation, the Lax pair is also derived. By introducing the new potential function, 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.

Keywords

• (2 + 1)-dimensional Kadomtsev–Petviashvili–Sawada–Kotera–Ramani equation
• Hirota’s bilinear operator
• binary Bell polynomials
• Hopf-Cole transformation
• Lax integrability
• soliton solutions