Bilinearization and fractional soliton dynamics of fractional Kadomtsev-Petviashvili equation

Abstract

Kadomtsev-Petviashvili equation is a mathematical model with many important applications in fluids. In this paper, a local fractional Kadomtsev-Petviashvili equation with Lax integrability is derived and solved by extending Hirota?s bilinear method. More specifically, the local fractional Kadomtsev-Petviashvili equation is derived from a local fractional Lax equation. With the help of a suitable transformation, the local fractional Kadomtsev-Petviashvili equation is then bilinearized. Based on the bilinearized form, n-soliton solution with Mittag-Leffler functions is obtained. In order to gain more insights into the fractional n-soliton solution, the velocity of the fractional one-soliton solution is simulated. It is shown that the velocity of the fractional one-soliton changes with the fractional order.