A variational approach to optical soliton collisions

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Abstract
The mathematical analogy between the nonlinear Schrödinger equations describing propagation of temporal soliton pulses in optical fibres, and propagation of spatial soliton beams in planar optical wave guides is discussed. A straightforward variational method, based on trial functions and Rayleigh-Ritz optimization, is demonstrated and applied to incoherent interaction of solitons. We study incoherent soliton interaction in a wavelength-multiplexed optical-fibre communication system, as well as the analogous problem for crossed optical beams in a planar waveguide. The predictions of the variational approach are also shown to be in good agreement with numerical simulation results and with experiments.