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EXACT SOLUTIONS WITH EXTERNAL LINEAR FUNCTIONS FOR THE POTENTIAL YU-TODA-SASA-FUKUYAMA EQUATION

ABSTRACT
Constructing exact solutions of non-linear PDE is of both theoretical and practical values. In this paper, a modified F-expansion method is proposed to construct exact solutions of non-linear PDE. To illustrate the validity and advantages of the proposed method, a (3+1)-D potential Yu-Toda-Sasa-Fukuyama equation is considered and more general exact solutions with external linear functions are obtained including Jacobi elliptic function solutions, hyperbolic function solutions, and trigonometric function solutions. It is shown that the original F-expansion method can not construct exact solutions of the potential Yu-Toda-Sasa-Fukuyama equation but the modified method is valid. The modified F-expansion method can lead to such exact solutions with external linear functions which possess a remarkable dynamical property, which is the solitary wave does not propagate in the horizontal direction as the traditional waves. The modified F-expansion method can be used for exactly solving some other non-linear PDE.
KEYWORDS
PAPER SUBMITTED: 2016-12-09
PAPER REVISED: 2017-09-28
PAPER ACCEPTED: 2017-09-28
PUBLISHED ONLINE: 2018-09-09
DOI REFERENCE: https://doi.org/10.2298/TSCI1804621Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE 4, PAGES [1621 - 1628]
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© 2018 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, 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