Vector rogue waves and dark-bright boomeronic solitons in autonomous and   non-autonomous settings
  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. 
R. B. Mareeswaran, E. G. Charalampidis, T. Kanna, P. G. Kevrekidis, D.   J. Frantzeskakis
nlin.PS