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Bilinearization and fractional soliton dynamics of fractional Kadomtsev-Petviashvili equation

Zhang Sheng (School of Mathematics and Physics, Bohai University, Jinzhou, China + Department of Mathemtics, Hohhot Minzu College, Hohhot, China)
Wei Yuanyuan (School of Mathematics and Physics, Bohai University, Jinzhou, China)
Xu Bo (School of Educational Science, Bohai University, Jinzhou, China)

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.

Keywords: local fractional Kadomtsev-Petviashvili equation, n-soliton solution, fractional soliton dynamics, Hirtoa’s bilinear method, Mittag-Leffler function