Numerical Investigation of the Nonlinear Schrödinger Equation with Saturation

M. A. Christou

doi:10.1063/1.3030777

Numerical Investigation of the Nonlinear Schrödinger Equation with Saturation

Research output: Contribution to journal › Conference article › peer-review

Abstract

We construct an implicit finite difference scheme to investigate numerically the nonlinear Schrödinger equation with saturation (NLSS). We use Newton's method to linearize the numerical scheme. We examine the propagation, interaction and overtake interaction of soliton solutions of the NLSS. Moreover, we examine the effect of the saturation term on the solution and compare it with the classical case of the cubic nonlinearity without saturation of nonlinearity. We track numerically the conserved properties and the phase shift experienced by the solitons upon collision.

Original language	English
Pages (from-to)	105-113
Number of pages	9
Journal	AIP Conference Proceedings
Volume	1067
Issue number	1
DOIs	https://doi.org/10.1063/1.3030777
Publication status	Published - 2008
Externally published	Yes
Event	34th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2008 - Sozopol, Bulgaria Duration: 8 Jun 2008 → 14 Jun 2008

Keywords

Christov difference scheme
discrete conservative properties
saturation
Schrodinger

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10.1063/1.3030777

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@article{60500e471f2e44b88103b62c00e4dd2e,

title = "Numerical Investigation of the Nonlinear Schr{\"o}dinger Equation with Saturation",

abstract = "We construct an implicit finite difference scheme to investigate numerically the nonlinear Schr{\"o}dinger equation with saturation (NLSS). We use Newton's method to linearize the numerical scheme. We examine the propagation, interaction and overtake interaction of soliton solutions of the NLSS. Moreover, we examine the effect of the saturation term on the solution and compare it with the classical case of the cubic nonlinearity without saturation of nonlinearity. We track numerically the conserved properties and the phase shift experienced by the solitons upon collision.",

keywords = "Christov difference scheme, discrete conservative properties, saturation, Schrodinger",

author = "Christou, {M. A.}",

note = "Funding Information: The author would like to express his gratitude to the Cyprus Research Promotion Foundation for support through Grant 4>IAONE/0506/01. Publisher Copyright: {\textcopyright} 2008 American Institute of Physics.; 34th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2008 ; Conference date: 08-06-2008 Through 14-06-2008",

year = "2008",

doi = "10.1063/1.3030777",

language = "English",

volume = "1067",

pages = "105--113",

journal = "AIP Conference Proceedings",

issn = "0094-243X",

publisher = "American Institute of Physics",

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T1 - Numerical Investigation of the Nonlinear Schrödinger Equation with Saturation

AU - Christou, M. A.

N1 - Funding Information: The author would like to express his gratitude to the Cyprus Research Promotion Foundation for support through Grant 4>IAONE/0506/01. Publisher Copyright: © 2008 American Institute of Physics.

PY - 2008

Y1 - 2008

N2 - We construct an implicit finite difference scheme to investigate numerically the nonlinear Schrödinger equation with saturation (NLSS). We use Newton's method to linearize the numerical scheme. We examine the propagation, interaction and overtake interaction of soliton solutions of the NLSS. Moreover, we examine the effect of the saturation term on the solution and compare it with the classical case of the cubic nonlinearity without saturation of nonlinearity. We track numerically the conserved properties and the phase shift experienced by the solitons upon collision.

AB - We construct an implicit finite difference scheme to investigate numerically the nonlinear Schrödinger equation with saturation (NLSS). We use Newton's method to linearize the numerical scheme. We examine the propagation, interaction and overtake interaction of soliton solutions of the NLSS. Moreover, we examine the effect of the saturation term on the solution and compare it with the classical case of the cubic nonlinearity without saturation of nonlinearity. We track numerically the conserved properties and the phase shift experienced by the solitons upon collision.

KW - Christov difference scheme

KW - discrete conservative properties

KW - saturation

KW - Schrodinger

UR - http://www.scopus.com/inward/record.url?scp=85058008406&partnerID=8YFLogxK

U2 - 10.1063/1.3030777

DO - 10.1063/1.3030777

M3 - Conference article

AN - SCOPUS:85058008406

SN - 0094-243X

VL - 1067

SP - 105

EP - 113

JO - AIP Conference Proceedings

JF - AIP Conference Proceedings

IS - 1

T2 - 34th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2008

Y2 - 8 June 2008 through 14 June 2008

ER -

Numerical Investigation of the Nonlinear Schrödinger Equation with Saturation

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Keywords

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