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Rapidity distribution within the defocusing non-linear Schrödinger equation model

Yasser Bezzaz, Léa Dubois, Isabelle Bouchoule

SciPost Phys. Core 6, 064 (2023) · published 26 September 2023


We consider the classical field integrable system whose evolution equation is the nonlinear Schrödinger equation with defocusing non-linearities, which is the classical limit of the quantum Lieb-Liniger model. We propose a simple derivation of the relation between two sets of conserved quantities: on the one hand the trace of the monodromy matrix, parameterized by the spectral parameter and introduced in the inverse-scattering framework, and on the other hand the rapidity distribution, a concept imported from the Lieb-Liniger model. To do so we use the definition of the rapidity distribution as the asymptotic momentum distribution after a very large expansion. We propose two different ways to derive the result, each one using a thought experiment that implements an expansion.

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