INTERACTION OF INITIALLY OVERLAPPING SOLITONS WITH DIFFERENT FREQUENCIES

We consider the problem of the interaction of initially overlapping so litons with different frequencies in the frame of scalar as well as Ve ctor nonlinear Schrodinger equations. By applying the inverse scatteri ng transform technique, we find the amplitude and the velocity of the formed solitons as a function of the initial conditions. In particular , for the scalar case we calculate the threshold values of the frequen cy separation Omega, when the solution transits from a two-soliton bou nd state to a one-soliton state (Omega = Omega(1)) and then back to a bound state (Omega = Omega(2)) and from a two-soliton bound state to a pair of escaping solitons (Omega = Omega(3)). If the initial frequenc y separation is less than the soliton spectral width, then perturbatio n theory may be applied. For other values of the frequency separation we calculate the soliton parameters numerically. the bifurcation point at Omega(3) disappears if the amplitudes of the initial pulses are no t equal. case we obtain similar results.