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

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arxiv nlin/0406059 v7 pith:AUGW7BD7 submitted 2004-06-25 nlin.SI math-phmath.MPnlin.CG

Ken-ichi Maruno , Gino Biondini This is my paper
classification nlin.SImath-phmath.MPnlin.CG
keywords discreteequationsultra-discretefullylatticeresonancesolitonsolutions
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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).

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  1. Two-dimensional Toda--Arnoldi correspondence: Holomorphic Krylov geometry and counterdiabatic transport

    quant-ph 2026-08 conditional novelty 5.0 of 10

    For non-Hermitian Hamiltonians, the Arnoldi diagonal and subdiagonal coefficients are the Flaschka variables of the finite two-dimensional Toda lattice, and their squares give both the Fubini-Study metric and the Berr...

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