Soliton trapping, transmission and wake in modulationally unstable media

TL;DR

This paper investigates how solitons interact with modulational instability structures in the focusing nonlinear Schrödinger equation, revealing regimes of transmission, trapping, and wake generation based on soliton velocity and background amplitude.

Contribution

It introduces a detailed analysis of soliton interactions with coherent structures, identifying conditions for trapping, transmission, and wake formation in modulationally unstable media.

Findings

Solitons can pass through or be trapped by coherent structures depending on velocity.

Trapped solitons change velocity but are not destroyed.

Generation of localized waves or wakes depends on eigenvalue position.

Abstract

Interactions between solitons and the coherent oscillation structures generated by localized disturbances via modulational instability are studied within the framework of the focusing nonlinear Schrodinger equation. Two main interaction regimes are identified based on the relative value of the velocity of the incident soliton compared to the amplitude of the background: soliton transmission and soliton trapping. Specifically, when the incident soliton velocity exceeds a certain threshold, the soliton passes through the coherent structure and emerges on the other side with its velocity unchanged. Conversely, when the incident soliton velocity is below the threshold, once the soliton enters the coherent structure, it remains confined there forever. It is demonstrated that the soliton is not destroyed, but its velocity inside the coherent structure is different from its initial one. Moreover, it is also shown that, depending on the location of the discrete eigenvalue associated to the soliton, these phenomena can also be accompanied by the generation of additional, localized propagating waves in the coherent structure, akin to a soliton-generated wake.