January  2007, 17(1): 121-132. doi: 10.3934/dcds.2007.17.121

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

1. 

Departamento de Métodos Matemáticos, Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68530, Rio de Janeiro, Brazil

2. 

Départament de Mathématiques, Université de Versailles Saint-Quentin, 45 avenue des États Unis, 78035 Versailles cedex, France

Received  August 2005 Revised  July 2006 Published  October 2006

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.
Citation: Rolci Cipolatti, Otared Kavian. On a nonlinear Schrödinger equation modelling ultra-short laser pulses with a large noncompact global attractor. Discrete and Continuous Dynamical Systems, 2007, 17 (1) : 121-132. doi: 10.3934/dcds.2007.17.121
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