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

Rolci Cipolatti; Otared Kavian

doi:10.3934/dcds.2007.17.121

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2007, Volume 17, Issue 1: 121-132. Doi: 10.3934/dcds.2007.17.121

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

Rolci Cipolatti^1, and
Otared Kavian^2,

1.
Departamento de Métodos Matemáticos, Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68530, Rio de Janeiro
2.
Départament de Mathématiques, Université de Versailles Saint-Quentin, 45 avenue des États Unis, 78035 Versailles cedex

Received: August 2005

Revised: July 2006

Published: January 2007

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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.

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Mathematics Subject Classification: Primary: 35Q35, 35Q60, 37K45.

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