TITLE:
Lie Group Classifications and Stability of Exact Solutions for Multidimensional Landau-Lifshitz Equations
AUTHORS:
Jiali Yu, Fuzhi Li, Hui Yang, Ganshan Yang
KEYWORDS:
Lie Group, Multidimensional Landau-Lifshitz Equation, Explicit Solutions, Stability
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.7,
April
28,
2016
ABSTRACT: In this paper, based on classical Lie group method, we study
multi-dimensional Landau-Lifshitz equation, and get its infinitesimal
generator, symmetry group and new solutions. In particular, we build the
connection between new exact solutions and old exact solutions. At the same
time, we also prove that the initial boundary value condition of the
three-dimensional Landau-Lifshitz equation admits a unique solution and discuss
the stability of the solution.