Multiscale expansion of the lattice sine--Gordon equation

Abstract

We expand a discrete--time lattice sine--Gordon equation on multiple lattices and obtain the partial difference equation which governs its far field behaviour. Such reduction allow us to obtain a new completely discrete nonlinear Schröedinger (NLS) type equation.

8 pages, Proceedings of the International Conference on Difference Equations, Special Functions and Applications held in Munich, 2005