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

Abstract

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

final version: several errors were corrected

References in corpus (4)

• On a family of solutions of the KP equation which also satisfy the Toda lattice hierarchy
• Simple strong glass forming models: mean-field solution with activation
• The tropical totally positive Grassmannian
• First steps in tropical geometry

Cited by in corpus (8)

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• A discrete variational identity on semi-direct sums of Lie algebras
• Multicomponent long-wave--short-wave resonance interaction system: Bright solitons, energy-sharing collisions, and resonant solitons
• Initial-boundary value problems for discrete evolution equations: discrete linear Schrodinger and integrable discrete nonlinear Schrodinger equations
• Matrix KP: tropical limit and Yang-Baxter maps
• An integrable generalization of the Toda law to the square lattice
• Tropical limit of matrix solitons and entwining Yang-Baxter maps
• Elastic and inelastic line-soliton solutions of the Kadomtsev-Petviashvili II equation