Numerical simulation of “limiting” envelope solitons of gravity waves on deep water

The results of numerical simulation of “limiting” envelope solitons of gravity waves on deep water (i.e., long-lived nonlinear groups including waves close to breaking) are reported. The existence of such quasi-soliton structures was demonstrated by Dyachenko and Zakharov [JETP Let. 88(5), 307 (2008)]. Solitary propagation and various types of interaction of limiting envelope solitons are considered with the help of numerical solution of the equations of ideal potential hydrodynamics in conformal variables. The results are compared with the description based on the generalized weakly nonlinear envelope equation (modified Dysthe model). It is shown that the initial conditions in the form of exact solutions to the nonlinear Schrödinger equation taking into account asymptotic corrections of the three orders corresponding to bound waves correctly describe limiting envelope solitons. The effects associated with the strongly nonlinear envelope soliton dynamics (instability of overly steep groups, short-wave envelope soliton destruction by a longwave group, and formation of coupled groups of waves) are revealed.