Multistability and localized attractors ina dissipative discrete NLS equation

Panayotis Panayotaros; Felipe Rivero

doi:10.3934/dcdsb.2014.19.1137

Article Contents

2014, Volume 19, Issue 4: 1137-1154. Doi: 10.3934/dcdsb.2014.19.1137

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Multistability and localized attractors in a dissipative discrete NLS equation

Panayotis Panayotaros^1, and
Felipe Rivero^2,

1.
Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F.
2.
Departamento de Matemática y Mecánica, I.I.M.A.S - U.N.A.M., Apdo. Postal 20-726, 01000 México D. F.

Received: May 31, 2013

Revised: November 30, 2013

Published: May 2014

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Abstract

We consider a finite discrete nonlinear Schrödinger equation with localized forcing, damping, and nonautonomous perturbations. In the autonomous case these systems are shown numerically to have multiple attracting spatially localized solutions. In the nonautonomous case we study analytically some properties of the pullback attractor of the system, assuming that the origin of the corresponding autonomous system is hyberbolic. We also see numerically the persistence of multiple localized attracting states under different types of nonautonomous perturbations.

Keywords:

Mathematics Subject Classification: Primary: 34D45, 37D05, 37F15; Secondary: 37B55.

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