Spatial frequency range analysis for the nonlinear Schrödinger equation

L. Z. Guo; Y. Z. Guo; S. A. Billings; D. Coca; Z. Q. Lang

doi:10.1007/s11071-014-1423-0

Spatial frequency range analysis for the nonlinear Schrödinger equation

L. Z. Guo^*
, Y. Z. Guo
, S. A. Billings
, D. Coca
, Z. Q. Lang

^*Corresponding author for this work

University of Sheffield

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

3 Scopus citations

Abstract

An analysis of the spatial frequency ranges for the nonlinear Schrödinger equation (NLS), subject to initial conditions with Gaussian and band-limited spatial frequency spectra, is presented in this paper. The analysis is based on a Volterra series representation of the NLS equation. This study reveals the relationship between the spatial frequency ranges of the solution, along with the evolution of the system, and the spatial frequency ranges of the initial conditions, and extends previous results in linear and nonlinear finite dimensional systems. The analysis also reveals a variety of nonlinear phenomena including self-phase modulation, cross-phase modulation and Raman effects modelled using the NLS equation.

Original language	English
Pages (from-to)	93-102
Number of pages	10
Journal	Nonlinear Dynamics
Volume	78
Issue number	1
DOIs	https://doi.org/10.1007/s11071-014-1423-0
State	Published - 7 Oct 2014
Externally published	Yes

Keywords

Frequency range
Spatial frequency
The nonlinear Schrodinger equation
Volterra series

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10.1007/s11071-014-1423-0

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title = "Spatial frequency range analysis for the nonlinear Schr{\"o}dinger equation",

abstract = "An analysis of the spatial frequency ranges for the nonlinear Schr{\"o}dinger equation (NLS), subject to initial conditions with Gaussian and band-limited spatial frequency spectra, is presented in this paper. The analysis is based on a Volterra series representation of the NLS equation. This study reveals the relationship between the spatial frequency ranges of the solution, along with the evolution of the system, and the spatial frequency ranges of the initial conditions, and extends previous results in linear and nonlinear finite dimensional systems. The analysis also reveals a variety of nonlinear phenomena including self-phase modulation, cross-phase modulation and Raman effects modelled using the NLS equation.",

keywords = "Frequency range, Spatial frequency, The nonlinear Schrodinger equation, Volterra series",

author = "Guo, \{L. Z.\} and Guo, \{Y. Z.\} and Billings, \{S. A.\} and D. Coca and Lang, \{Z. Q.\}",

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doi = "10.1007/s11071-014-1423-0",

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T1 - Spatial frequency range analysis for the nonlinear Schrödinger equation

AU - Guo, L. Z.

AU - Guo, Y. Z.

AU - Billings, S. A.

AU - Coca, D.

AU - Lang, Z. Q.

PY - 2014/10/7

Y1 - 2014/10/7

N2 - An analysis of the spatial frequency ranges for the nonlinear Schrödinger equation (NLS), subject to initial conditions with Gaussian and band-limited spatial frequency spectra, is presented in this paper. The analysis is based on a Volterra series representation of the NLS equation. This study reveals the relationship between the spatial frequency ranges of the solution, along with the evolution of the system, and the spatial frequency ranges of the initial conditions, and extends previous results in linear and nonlinear finite dimensional systems. The analysis also reveals a variety of nonlinear phenomena including self-phase modulation, cross-phase modulation and Raman effects modelled using the NLS equation.

AB - An analysis of the spatial frequency ranges for the nonlinear Schrödinger equation (NLS), subject to initial conditions with Gaussian and band-limited spatial frequency spectra, is presented in this paper. The analysis is based on a Volterra series representation of the NLS equation. This study reveals the relationship between the spatial frequency ranges of the solution, along with the evolution of the system, and the spatial frequency ranges of the initial conditions, and extends previous results in linear and nonlinear finite dimensional systems. The analysis also reveals a variety of nonlinear phenomena including self-phase modulation, cross-phase modulation and Raman effects modelled using the NLS equation.

KW - Frequency range

KW - Spatial frequency

KW - The nonlinear Schrodinger equation

KW - Volterra series

UR - https://www.scopus.com/pages/publications/84919877685

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DO - 10.1007/s11071-014-1423-0

M3 - 文章

AN - SCOPUS:84919877685

SN - 0924-090X

VL - 78

SP - 93

EP - 102

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

IS - 1

ER -

Spatial frequency range analysis for the nonlinear Schrödinger equation

Abstract

Keywords

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