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.
@article{arxiv.1407.1336,
title = {Vector rogue waves and dark-bright boomeronic solitons in autonomous and non-autonomous settings},
author = {R. B. Mareeswaran and E. G. Charalampidis and T. Kanna and P. G. Kevrekidis and D. J. Frantzeskakis},
journal= {arXiv preprint arXiv:1407.1336},
year = {2014}
}