Resonance and web structure in discrete soliton systems: the two-dimensional Toda lattice and its fully discrete and ultra-discrete analogues

Abstract

We present a class of solutions of the two-dimensional Toda lattice equation,\nits fully discrete analogue and its ultra-discrete limit. These solutions\ndemonstrate the existence of soliton resonance and web-like structure in\ndiscrete integrable systems such as differential-difference equations,\ndifference equations and cellular automata (ultra-discrete equations).\n