TY - JOUR
TI - A new approach for finding standard heat equation and a special Newell-whitehead equation
AU - Guo Xiu-Rong
AU - Zhang Yu-Feng
AU - Guo Mei
AU - Liu Zheng-Tao
JN - Thermal Science
PY - 2019
VL - 23
IS - 3
SP - 1629
EP - 1636
PT - Article
AB - 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.