PARAMETRIC ENVELOPE SOLITONS IN COUPLED KORTEWEG-DE-VRIES EQUATIONS

We demonstrate that a system of linearly coupled Korteweg-de Vries equ ations, which inter alia is a general model of resonantly coupled inte rnal waves in a stratified fluid, can give rise to broad envelope soli tons produced by a double phase- and group-velocity resonance between the fundamental and second harmonics for certain wavenumbers. We deriv e asymptotic equations for the amplitudes of the two harmonics, which are identical to the second-harmonic-generation equations in a diffrac tive medium, that have recently attracted a lot of attention in nonlin ear optics and give rise to the so-called parametric solitons. To chec k if the predicted solitons are close to exact solutions of the couple d Korteweg-de Vries equations, we perform direct numerical simulations , with initial conditions suggested by the above-mentioned parametric- soliton solution to the asymptotic equations. Since the latter is know n only in a numerical form, we use for them a recently developed analy tical variational approximation. As a result, we observe very long-liv ed steadily propagating wave packets generated by these initial condit ions. Thus we fmd a physical system that may allow experimental observ ation of propagating parametric solitons, while in nonlinear optics th ey are observed only as spatial solitons.