Vector rogue waves and dark-bright boomeronic solitons in autonomous and non-autonomous settings

TL;DR

This paper investigates vector rogue waves and dark-bright boomeronic solitons in two-component nonlinear Schrödinger equations with time-dependent coefficients, revealing their dynamics and stability through similarity transformations and numerical simulations.

Contribution

It introduces a method to derive vector rogue waves and dark-bright boomeronic solitons in non-autonomous systems using similarity transformations to the integrable Manakov system.

Findings

Rogue wave formation often leads to modulational instability and soliton train emergence.

Different dynamical scenarios beyond the typical phenomenology are identified.

Numerical simulations confirm the theoretical predictions.

Abstract

In this work, we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schr\"odinger equations with various physically motivated time-dependent nonlinearity coefficients, as well as spatio-temporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark-bright boomeron-like soliton solutions of the latter are converted back into ones of the original non-autonomous model. Using direct numerical simulations we find that, in most cases, the rogue wave formation is rapidly followed by a modulational instability that leads to the emergence of an expanding soliton train. Scenarios different than this generic phenomenology are also reported.