On the Dynamics of the Classical Transverse Field Ising Chain
Author: Johann, A.
Source: Journal of Differential Equations, Volume 184, Number 1, September 2002 , pp. 224-258(35)
Publisher: Academic Press
Abstract:We investigate stationary and travelling wave solutions of a special lattice differential equation in one space dimension. Depending on a parameter , results are given on the existence, shape and stability for these kind of solutions. The analysis of travelling wave solutions leads us to a functional differential equation with both forward and backward shifts. The existence of solutions of this equation will be proved by use of the implicit function theorem. In particular, we consider kink solutions and periodic solutions. © 2002 Elsevier Science (USA).
Document Type: Research Article
Affiliations: Technische Universität München, Zentrum Mathematik, München, D-80290, Germany
Publication date: September 1, 2002