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Simulation of instability of bright solitons for NLS with saturating nonlinearity. (English) Zbl 0972.78019

Summary: The paper deals with the generalized 1+1 nonlinear Schrödinger equation \(iu_t+u_{xx}+|u|^{2p}u-\alpha|u|^{2q}u=0\), \(\alpha<0\), \(q>p\), which is the model of laser propagation throughout nonlinear optic materials with a saturation. We focus on the numerical study of the effect of soliton’s “self-compression” under small perturbations and on the trapping phenomena due to collisions.

MSC:

78A60 Lasers, masers, optical bistability, nonlinear optics
35Q60 PDEs in connection with optics and electromagnetic theory
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