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On a nonlinear Schrödinger equation modelling ultra-short laser pulses with a large noncompact global attractor

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  • We study a Schrödinger equation with a nonlocal nonlinearity, which has been considered as a model for ultra-short laser pulses. An interesting feature of this equation is that the underlying dynamical system possesses a bounded non compact global attractor, actually a ball in $L^2(R)$. Existence and instability of standing waves are also proved.
    Mathematics Subject Classification: Primary: 35Q35, 35Q60, 37K45.


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