  Nonlinear dynamics of surface gravity waves trapped by an opposing jet
current is studied analytically and numerically. For wave fields narrowband in
frequency but not necessarily with narrow angular distributions the developed
asymptotic weakly nonlinear theory based on the modal approach of (V. Shrira,
A. Slunyaev, J. Fluid. Mech, 738, 65, 2014) leads to the one-dimensional
modified nonlinear Schr\"{o}dinger equation of self-focusing type for a single
mode. Its solutions such as envelope solitons and breathers are considered to
be prototypes of rogue waves; these solutions, in contrast to waves in the
absence of currents, are robust with respect to transverse perturbations, which
suggests potentially higher probability of rogue waves. Robustness of the
long-lived analytical solutions in form of the modulated trapped waves and
solitary wave groups is verified by direct numerical simulations of potential
Euler equations.
