Recurrence due to periodic multi-soliton fission in the defocusing nonlinear Schrodinger equation

TL;DR

This paper investigates the universality of recurrence phenomena caused by multisoliton fission in the defocusing nonlinear Schrödinger equation, providing analytical predictions for soliton features and comparing with the Korteweg-de Vries model.

Contribution

It offers a full analytical prediction of soliton emergence and recurrence in the semiclassical defocusing nonlinear Schrödinger equation, extending understanding of universality in nonlinear wave dynamics.

Findings

Predicted number and features of solitons post-breaking.

Demonstrated near-recurrences and their universal aspects.

Identified differences between NLS and KdV models due to velocity scaling.

Abstract

We address the degree of universality of the Fermi-Pasta-Ulam recurrence induced by multisoliton fission from a harmonic excitation by analysing the case of the semiclassical defocusing nonlinear Schrodinger equation, which models nonlinear wave propagation in a variety of physical settings. Using a suitable Wentzel-Kramers-Brillouin approach to the solution of the associated scattering problem we accurately predict, in full analytical way, the number and the features (amplitude and velocity) of soliton-like excitations emerging post-breaking, as a function of the dispersion smallness parameter. This also permits to predict and analyse the near-recurrences, thereby inferring the universal character of the mechanism originally discovered for the Korteweg-deVries equation. We show, however, that important differences exist between the two models, arising from the different scaling rules obeyed by the soliton velocities.