On localization in the discrete nonlinear Schrödinger equation

O. Bang; J. Juul Rasmussen; P.L. Christiansen

doi:10.1016/0167-2789(93)90042-Y

On localization in the discrete nonlinear Schrödinger equation

O. Bang, J. Juul Rasmussen, P.L. Christiansen

Research output: Contribution to journal › Journal article › Research

Abstract

For some values of the grid resolution, depending on the nonlinearity, the discrete nonlinear Schrodinger equation with arbitrary power nonlinearity can be approximated by the corresponding continuum version of the equation. When the discretization becomes too coarse, the discrete equation exhibits localization in regimes where blow-up cannot occur in the continuum system. This phenomenon is investigated numerically, and the grid resolution at which the transition occurs is determined.

Original language	English
Journal	Physica D: Nonlinear Phenomena
Volume	68
Issue number	1
Pages (from-to)	169-173
ISSN	0167-2789
DOIs	https://doi.org/10.1016/0167-2789(93)90042-Y
Publication status	Published - 1993

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title = "On localization in the discrete nonlinear Schr{\"o}dinger equation",

abstract = "For some values of the grid resolution, depending on the nonlinearity, the discrete nonlinear Schrodinger equation with arbitrary power nonlinearity can be approximated by the corresponding continuum version of the equation. When the discretization becomes too coarse, the discrete equation exhibits localization in regimes where blow-up cannot occur in the continuum system. This phenomenon is investigated numerically, and the grid resolution at which the transition occurs is determined. ",

keywords = "Fremtidig energiteknologi",

author = "O. Bang and {Juul Rasmussen}, J. and P.L. Christiansen",

year = "1993",

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T1 - On localization in the discrete nonlinear Schrödinger equation

AU - Bang, O.

AU - Juul Rasmussen, J.

AU - Christiansen, P.L.

PY - 1993

Y1 - 1993

N2 - For some values of the grid resolution, depending on the nonlinearity, the discrete nonlinear Schrodinger equation with arbitrary power nonlinearity can be approximated by the corresponding continuum version of the equation. When the discretization becomes too coarse, the discrete equation exhibits localization in regimes where blow-up cannot occur in the continuum system. This phenomenon is investigated numerically, and the grid resolution at which the transition occurs is determined.

AB - For some values of the grid resolution, depending on the nonlinearity, the discrete nonlinear Schrodinger equation with arbitrary power nonlinearity can be approximated by the corresponding continuum version of the equation. When the discretization becomes too coarse, the discrete equation exhibits localization in regimes where blow-up cannot occur in the continuum system. This phenomenon is investigated numerically, and the grid resolution at which the transition occurs is determined.

KW - Fremtidig energiteknologi

U2 - 10.1016/0167-2789(93)90042-Y

DO - 10.1016/0167-2789(93)90042-Y

M3 - Journal article

VL - 68

SP - 169

EP - 173

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1

ER -