Large variations in NLS bi-soliton wave groups

The nonlinear Schrödinger (NLS) equation describes the spatial–temporal evolution of the complex amplitude of wave groups in beams and pulses in both second and third order nonlinear material. In this paper we investigate in detail the wave group that has the exact two-soliton solution as amplitude, and show that large variations in the amplitude appear to form a pattern that, at the peak interaction, resembles quite well the linear superposition. The complexity of the phenomenon is a combination of nonlinear effects and linear interference of the carrier waves: the characteristic parameter is the quotient of wave amplitude and frequency difference of the carrier waves, which is also proportional to the quotient of the modulation period of the carrier waves during interaction and the interaction period of the soliton envelopes.