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

Rolci Cipolatti, Otared Kavian

Type: Article

Publication Date: 2007-01-01

Citations: 2

DOI: https://doi.org/10.3934/dcds.2007.17.121

Abstract

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.

Locations

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+	Semigroups of Linear Operators and Applications to Partial Differential Equations	1983	A. Pazy
+	Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations	1977	Robert S. Strichartz
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