THERMAL SCIENCE

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Sheng Zhang

,

Yuanyuan Wei

,

Bo Xu

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.
KEYWORDS
LFKP equation, n-soliton solution, fractional soliton dynamics, Hirtoa’s bilinear method, Mittag-Leffler function
PAPER SUBMITTED: 2018-08-15
PAPER REVISED: 2018-11-21
PAPER ACCEPTED: 2019-01-24
PUBLISHED ONLINE: 2019-05-26
DOI REFERENCE: https://doi.org/10.2298/TSCI180815207Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 3, PAGES [1425 - 1431]
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Bilinearization and fractional soliton dynamics of fractional Kadomtsev-Petviashvili equation

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence