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

Abstract

In this work, we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schrödinger 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.

15 pages, 8 figures, 1 table

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• Dynamical stabilization of two-dimensional trapless Bose-Einstein condensates by three-body interaction and quantum fluctuations
• Manipulation of vector solitons in a system of inhomogeneous coherently coupled nonlinear Schrödinger models with variable nonlinearities
• Amplification of matter rogue waves and breathers in quasi-two-dimensional Bose-Einstein condensates
• Bright Matter-Wave Bound Soliton Molecules in Spin-1 Bose-Einstein Condensates with Non-autonomous Nonlinearities
• Nonlinear bandgap transmission by discrete rogue waves induced in a pendulum chain