Particle Scattering and Fusion for the Ablowitz-Ladik Chain

Abstract

The Ablowitz-Ladik chain is an integrable discretized version of the nonlinear Schrödinger equation. We report on a novel underlying Hamiltonian particle system with properties similar to the ones known for the classical Toda chain and Calogero fluid with $1/{\sinh }^2$ pair interaction. Boundary conditions are imposed such that, both in the distant past and future, particles have a constant velocity. We establish the many-particle scattering for the Ablowitz-Ladik chain and obtain properties known for generic integrable many-body systems. For a specific choice of the chain, real initial data remain real in the course of time. Then, asymptotically, particles move in pairs with a velocity-dependent size and scattering shifts are governed by the fusion rule.

arXiv comment32 pages, 5 figures, 2 appendices

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Cited by in corpus (2)

• Hydrodynamics of spin transport in the Haldane-Shastry chain
• Lax random matrices from Calogero systems