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Exact numerical solutions for dark waves on the discrete nonlinear Schrödinger equation

Opened Access Exact numerical solutions for dark waves on the discrete nonlinear Schrödinger equation

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Autor: Sánchez-Rey, Bernardo
Johansson, Magnus
Departamento: Universidad de Sevilla. Departamento de Física Aplicada I
Fecha: 2005
Publicado en: Physical Review E, 71(3), 036627: 1-11
Tipo de documento: Artículo
Resumen: In this paper we study numerically existence and stability of exact dark waves on the (nonintegrable) discrete nonlinear Schrödinger equation for a finite one-dimensional lattice. These are solutions that bifurcate from stationary dark modes with constant background intensity and zero intensity at a site, and whose initial state translates exactly one site each period of the internal oscillations. We show that exact dark waves are characterized by an oscillatory background whose wavelength is closely related with the velocity. Faster dark waves require smaller wavelengths. For slow enough velocity dark waves are linearly stable, but when trying to continue numerically a solution towards higher velocities bifurcations appear, due to rearrangements in the oscillatory tail in order to make possible a decreasing of the wavelength. However, in principle, one might control the stability of an exact dark wave adjusting a phase factor which plays the role of a discreteness parameter. In addit...
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Cita: Sánchez-Rey, B. y Johansson, M. (2005). Exact numerical solutions for dark waves on the discrete nonlinear Schrödinger equation. Physical Review E, 71 (3), 036627-1-11.
Tamaño: 202.0Kb
Formato: PDF

URI: http://hdl.handle.net/11441/25604

DOI: 10.1103/PhysRevE.71.036627

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