## THERMAL SCIENCE

International Scientific Journal

### 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

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**Issue 4**, PAGES [1621 - 1628]

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