## 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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### References:

 [1] Bona, J.L.; Soyer, A., On the stability of solitory-wave solutions of model equations for long waves, J. nonlinear sci., 4, 449-470, (1994) · Zbl 0809.35095 [2] Buslaev, V.S.; Perelman, G.S., Scattering for the nonlinear Schrödinger equation: states that are close to a soliton, Algebra anal., 4, 63-102, (1992) · Zbl 0853.35112 [3] LeMesurier, B.J.; Papanicolaou, G.; Sulem, C.; Sulem, P.L., Focusing and multi-focusing solutions of the nonlinear Schrödinger equation, Phys. D, 31, 78-102, (1988) · Zbl 0694.35196 [4] Pelinovsky, D.E., Radiative effects to the adiabatic dynamics of envelop-wave solitons, Phys. D, 119, 301-313, (1998) · Zbl 1194.35423 [5] Pelinovsky, D.E.; Afanasjev, V.V.; Kivshar, Yu.S., Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized nonlinear sclirödinger equation, Phys. rev., E-53, 1940-1953, (1996) [6] Pelinovsky, D.E.; Afanasjev, V.V.; Kivshar, Yu.S., Internal modes of envelope solitons, Phys. D, 116, 121-142, (1998) · Zbl 0934.35175 [7] Strauss, W.A., Existence of solitory waves in higher dimensions, Comm. math. phys., 55, 149-162, (1977) · Zbl 0356.35028
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