Dynamics in discrete two-dimensional nonlinear Schrödinger equations in the presence of point defects

Peter Leth Christiansen; Yuri Borisovich Gaididei; Kim Rasmussen; Vladimir Mezentsev; Jens Juul Rasmussen

doi:10.1103/PhysRevB.54.900

Dynamics in discrete two-dimensional nonlinear Schrödinger equations in the presence of point defects

Peter Leth Christiansen, Yuri Borisovich Gaididei, Kim Rasmussen, Vladimir Mezentsev, Jens Juul Rasmussen

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Abstract

The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity and point impurities is taken into account. The stability properties of the stationary solutions are examined. The essential importance of the existence of stable immobile solitons in the two-dimensional dynamics of the traveling pulses is demonstrated. The typical scenario of the two-dimensional quasicollapse of a moving intense pulse represents the formation of standing trapped narrow spikes. The influence of the point impurities on this dynamics is also investigated.

Original language	English
Journal	Physical Review B
Volume	54
Issue number	2
Pages (from-to)	900-912
ISSN	2469-9950
DOIs	https://doi.org/10.1103/PhysRevB.54.900
Publication status	Published - 1996

Bibliographical note

Copyright (1996) American Physical Society.

Keywords

LOCALIZED MODES
ENERGY-TRANSFER

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title = "Dynamics in discrete two-dimensional nonlinear Schr{\"o}dinger equations in the presence of point defects",

abstract = "The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity and point impurities is taken into account. The stability properties of the stationary solutions are examined. The essential importance of the existence of stable immobile solitons in the two-dimensional dynamics of the traveling pulses is demonstrated. The typical scenario of the two-dimensional quasicollapse of a moving intense pulse represents the formation of standing trapped narrow spikes. The influence of the point impurities on this dynamics is also investigated.",

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note = "Copyright (1996) American Physical Society.",

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T1 - Dynamics in discrete two-dimensional nonlinear Schrödinger equations in the presence of point defects

AU - Christiansen, Peter Leth

AU - Gaididei, Yuri Borisovich

AU - Rasmussen, Kim

AU - Mezentsev, Vladimir

AU - Juul Rasmussen, Jens

PY - 1996

Y1 - 1996

N2 - The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity and point impurities is taken into account. The stability properties of the stationary solutions are examined. The essential importance of the existence of stable immobile solitons in the two-dimensional dynamics of the traveling pulses is demonstrated. The typical scenario of the two-dimensional quasicollapse of a moving intense pulse represents the formation of standing trapped narrow spikes. The influence of the point impurities on this dynamics is also investigated.

AB - The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity and point impurities is taken into account. The stability properties of the stationary solutions are examined. The essential importance of the existence of stable immobile solitons in the two-dimensional dynamics of the traveling pulses is demonstrated. The typical scenario of the two-dimensional quasicollapse of a moving intense pulse represents the formation of standing trapped narrow spikes. The influence of the point impurities on this dynamics is also investigated.

KW - LOCALIZED MODES

KW - ENERGY-TRANSFER

U2 - 10.1103/PhysRevB.54.900

DO - 10.1103/PhysRevB.54.900

M3 - Journal article

SN - 2469-9950

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EP - 912

JO - Physical Review B

JF - Physical Review B

IS - 2

ER -

Dynamics in discrete two-dimensional nonlinear Schrödinger equations in the presence of point defects

Abstract

Bibliographical note

Keywords

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