  Rogue waves are known to be much more common on jet currents. A possible
explanation was put forward in [ [V. Shrira and A. Slunyaev, Nonlinear dynamics
of trapped waves on jet currents and rogue waves, Phys. Rev. E 89, 041002,
2014]]: for the waves trapped on a current robust long-lived envelope solitary
waves localized in both horizontal directions become possible, such wave
patterns cannot exist in the absence of the current. In this work we
investigate interactions between envelope solitons of essentially nonlinear
trapped waves by means of the direct numerical simulation of the Euler
equations. The solitary waves remain localized in both horizontal directions
for hundreds of wave periods. We also demonstrate a high efficiency of the
developed analytic nonlinear mode theory for description of the long-lived
solitary patterns up to remarkably steep waves. We show robustness of the
solitons in the course of interactions, and the possibility of extreme wave
generation as a result of solitons' collisions. Their collisions are shown to
be nearly elastic. These robust solitary waves obtained from the Euler
equations without weak nonlinearity assumptions are viewed as a plausible model
of rogue waves on jet currents.
