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Bilinearization and fractional soliton dynamics of fractional Kadomtsev-Petviashvili equation

Kadomtsev-Petviashvili (KP) equation is a mathematical model with many important applications in fluids. In this paper, a local fractional KP (LFKP) equation with Lax integrability is derived and solved by extending Hirota’s bilinear method. More specifically, the LFKP equation is derived from a local fractional Lax equation. With the help of a suitable transformation, the LFKP 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
PAPER REVISED: 2018-11-21
PAPER ACCEPTED: 2019-01-24
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