Abstract
An extended nonlinear Schrodinger equation, with positive fourth-order dispersion and a quintic nonlinearity, is shown to possess a soliton-like solution which exists in resonance with linear dispersive waves, but emits no radiation at all. When this solution is perturbed the emission of radiation begins. An approximate variational analysis and direct numerical integrations are carried out to show that this soliton-like solution is robust enough to resist small perturbations without being dispersed away. Initial conditions which are close to the exact solution evolve into quasi-stationary solutions which emit radiation, but maintain their shapes over extremely long distances.
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