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arXiv · 2404.07095

Particle Scattering and Fusion for the Ablowitz-Ladik Chain

Alberto Brollo·Herbert Spohn
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Abstract

The Ablowitz-Ladik chain is an integrable discretized version of the nonlinear Schr\"{o}dinger 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.

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BibTeXRIS

Alberto Brollo, Herbert Spohn. 2024-04-10. Particle Scattering and Fusion for the Ablowitz-Ladik Chain. https://doi.org/10.1088/1751-8121/ad6411

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