American Institute of Mathematical Sciences

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 & Continuous Dynamical Systems, 2007, 17 (1) : 121-132. doi: 10.3934/dcds.2007.17.121
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