We prove global existence and uniqueness of solutions for a modified nonlinear Schrödinger equation modelling pulse propagation in an optical fibre laser. Pulse shaping is achieved by a saturable Bragg reflector: a device modelled here by nonlocal, nonlinear terms. Our results rely only on general model properties and are not limited to the specific case discussed. We discuss stability and bifurcation from the trivial solution and chirped soliton solutions in a special case. Numerical illustrations are provided.
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Mielke et al. (1998) studied this question.
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