## THERMAL SCIENCE

International Scientific Journal

### A NEW APPROACH FOR FINDING STANDARD HEAT EQUATION AND A SPECIAL NEWELL-WHITEHEAD EQUATION

**ABSTRACT**

Under a frame of 2 × 2 matrix Lie algebras, Tu and Meng [9] once established a united integrable model of the Ablowitz-Kaup-Newel-Segur (AKNS) hierarchy, the D-AKNS hierarchy, the Levi hierarchy and the TD hierarchy. Based on this idea, we introduce two block-matrix Lie algebras to present an isospectral problem, whose compatibility condition gives rise to a type of integrable hierarchy which can be reduced to the Levi hierarchy and the AKNS hierarchy, and so on. A united integrable model obtained by us in the paper is different from that given by Tu and Meng. Specially, the main result in the paper can be reduced to two new various integrable couplings of the Levi hierarchy, from which we again obtain the standard heat equation and a special Newell-Whitehead equation.

**KEYWORDS**

PAPER SUBMITTED: 2018-12-19

PAPER REVISED: 2019-01-01

PAPER ACCEPTED: 2019-01-15

PUBLISHED ONLINE: 2019-05-26

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**3**, PAGES [1629 - 1636]

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