Peierls–Nabarro potential profile of discrete nonlinear Schrödinger equation

U. Al Khawaja; S. M. Al-Marzoug; H. Bahlouli

doi:10.1016/j.cnsns.2016.10.019

Peierls–Nabarro potential profile of discrete nonlinear Schrödinger equation

U. Al Khawaja^*
, S. M. Al-Marzoug
, H. Bahlouli

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We derive an analytic formula for the Peierls–Nabarro (PN) potential of a discrete nonlinear Schro¨dinger equation with cubic focusing nonlinearity. The potential is given in terms of the ratio between the strength of nonlinearity and dispersion spanning the whole range between strongly localised to smoothly moving solitons. The essential features that characterize the on-site and inter-site stationary states are obtained. The soliton's center-of-mass dynamics is also described. The derivation is performed variationaly using two trial functions with good agreement with the exact numerical calculation.

Original language	English
Pages (from-to)	74-80
Number of pages	7
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	46
DOIs	https://doi.org/10.1016/j.cnsns.2016.10.019
State	Published - 1 May 2017

Bibliographical note

Publisher Copyright:
© 2016

Keywords

Discrete solitons
Pierls–Nabarro potential

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Applied Mathematics

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10.1016/j.cnsns.2016.10.019

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title = "Peierls–Nabarro potential profile of discrete nonlinear Schr{\"o}dinger equation",

abstract = "We derive an analytic formula for the Peierls–Nabarro (PN) potential of a discrete nonlinear Schro¨dinger equation with cubic focusing nonlinearity. The potential is given in terms of the ratio between the strength of nonlinearity and dispersion spanning the whole range between strongly localised to smoothly moving solitons. The essential features that characterize the on-site and inter-site stationary states are obtained. The soliton's center-of-mass dynamics is also described. The derivation is performed variationaly using two trial functions with good agreement with the exact numerical calculation.",

keywords = "Discrete solitons, Pierls–Nabarro potential",

author = "\{Al Khawaja\}, U. and Al-Marzoug, \{S. M.\} and H. Bahlouli",

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year = "2017",

month = may,

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doi = "10.1016/j.cnsns.2016.10.019",

language = "English",

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TY - JOUR

T1 - Peierls–Nabarro potential profile of discrete nonlinear Schrödinger equation

AU - Al Khawaja, U.

AU - Al-Marzoug, S. M.

AU - Bahlouli, H.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - We derive an analytic formula for the Peierls–Nabarro (PN) potential of a discrete nonlinear Schro¨dinger equation with cubic focusing nonlinearity. The potential is given in terms of the ratio between the strength of nonlinearity and dispersion spanning the whole range between strongly localised to smoothly moving solitons. The essential features that characterize the on-site and inter-site stationary states are obtained. The soliton's center-of-mass dynamics is also described. The derivation is performed variationaly using two trial functions with good agreement with the exact numerical calculation.

AB - We derive an analytic formula for the Peierls–Nabarro (PN) potential of a discrete nonlinear Schro¨dinger equation with cubic focusing nonlinearity. The potential is given in terms of the ratio between the strength of nonlinearity and dispersion spanning the whole range between strongly localised to smoothly moving solitons. The essential features that characterize the on-site and inter-site stationary states are obtained. The soliton's center-of-mass dynamics is also described. The derivation is performed variationaly using two trial functions with good agreement with the exact numerical calculation.

KW - Discrete solitons

KW - Pierls–Nabarro potential

UR - https://www.scopus.com/pages/publications/84994246880

U2 - 10.1016/j.cnsns.2016.10.019

DO - 10.1016/j.cnsns.2016.10.019

M3 - Article

AN - SCOPUS:84994246880

SN - 1007-5704

VL - 46

SP - 74

EP - 80

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

ER -

Peierls–Nabarro potential profile of discrete nonlinear Schrödinger equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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