Interaction of initially overlapping solitons with different frequencies

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Abstract
We consider the problem of the interaction of initially overlapping solitons with different frequencies in the frame of scalar as well as vector nonlinear Schrödinger equations. By applying the inverse scattering 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 frequency separation Ω, when the solution transits from a two-soliton bound state to a one-soliton state (Ω = Ω1) and then back to a bound state (Ω = Ω2) and from a two-soliton bound state to a pair of escaping solitons (Ω = Ω3). If the initial frequency separation is less than the soliton spectral width, then perturbation theory may be applied. For other values of the frequency separation we calculate the soliton parameters numerically. We show that the bifurcation point at Ω3 disappears if the amplitudes of the initial pulses are not equal. For the vector case we obtain similar results.