## THERMAL SCIENCE

International Scientific Journal

### DARBOUX TRANSFORM AND CONSERVATION LAWS OF NEW DIFFERENTIAL-DIFFERENCE EQUATIONS

**ABSTRACT**

Darboux transforms, exact solutions and conservation laws are important topics in thermal science and other fields as well. In this paper, the new non-linear differential-difference equations associated a discrete linear spectral problem are studied analytically. Firstly, the Darboux transform of the studied equations is constructed, and exact solutions are then obtained. Finally, infinite many conservation laws are derived.

**KEYWORDS**

PAPER SUBMITTED: 2019-04-28

PAPER REVISED: 2019-08-10

PAPER ACCEPTED: 2019-09-08

PUBLISHED ONLINE: 2020-06-21

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**Issue 4**, PAGES [2519 - 2527]

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