THERMAL SCIENCE

International Scientific Journal

Xiu-Rong Guo

,

Yu-Feng Zhang

,

Mei Guo

,

Zheng-Tao Liu

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
Lie algebra, TAH scheme, DS hierarchy, heat equation, Newell-Whitehead equation
PAPER SUBMITTED: 2018-12-19
PAPER REVISED: 2019-01-01
PAPER ACCEPTED: 2019-01-15
PUBLISHED ONLINE: 2019-05-26
DOI REFERENCE: https://doi.org/10.2298/TSCI181219233G
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 3, PAGES [1629 - 1636]
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A new approach for finding standard heat equation and a special Newell-whitehead 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