Modulational instability analysis of the Peregrine soliton

U. Al Khawaja; H. Bahlouli; M. Asad-uz-zaman; S. M. Al-Marzoug

doi:10.1016/j.cnsns.2014.01.002

Modulational instability analysis of the Peregrine soliton

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

^*Corresponding author for this work

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

17 Scopus citations

Abstract

We perform modulational instability analysis of the Peregrine soliton. The eigensystem of the linearized perturbations results in time-dependent gain curve. The instantaneous stability of the Peregrine soliton is studied at different times and in terms of modulated spacial width. A correlation between the most unstable eigenmode and the time evolution of the Peregrine soliton is established. Our analysis explains the bifurcation of the Peregrine soliton into Ma breathers and the generation of shock waves. The theoretical approach and numerical procedure followed here may be applied to any other localized solution with nontrivial time dependence.

Original language	English
Pages (from-to)	2706-2714
Number of pages	9
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	19
Issue number	8
DOIs	https://doi.org/10.1016/j.cnsns.2014.01.002
State	Published - Aug 2014

Bibliographical note

Funding Information:
The authors acknowledge the support provided by United Arab Emirates University under the NRF grant UAEU-NRF-2011 and the support provided by King Fahd University of Petroleum and Minerals under group project Nos. RG1217-1, RG1217-2, RG1214-1, and RG1214-2.

Keywords

Modulational instability
Peregrine

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Applied Mathematics

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10.1016/j.cnsns.2014.01.002

Cite this

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title = "Modulational instability analysis of the Peregrine soliton",

abstract = "We perform modulational instability analysis of the Peregrine soliton. The eigensystem of the linearized perturbations results in time-dependent gain curve. The instantaneous stability of the Peregrine soliton is studied at different times and in terms of modulated spacial width. A correlation between the most unstable eigenmode and the time evolution of the Peregrine soliton is established. Our analysis explains the bifurcation of the Peregrine soliton into Ma breathers and the generation of shock waves. The theoretical approach and numerical procedure followed here may be applied to any other localized solution with nontrivial time dependence.",

keywords = "Modulational instability, Peregrine",

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note = "Funding Information: The authors acknowledge the support provided by United Arab Emirates University under the NRF grant UAEU-NRF-2011 and the support provided by King Fahd University of Petroleum and Minerals under group project Nos. RG1217-1, RG1217-2, RG1214-1, and RG1214-2. ",

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doi = "10.1016/j.cnsns.2014.01.002",

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T1 - Modulational instability analysis of the Peregrine soliton

AU - Al Khawaja, U.

AU - Bahlouli, H.

AU - Asad-uz-zaman, M.

AU - Al-Marzoug, S. M.

N1 - Funding Information: The authors acknowledge the support provided by United Arab Emirates University under the NRF grant UAEU-NRF-2011 and the support provided by King Fahd University of Petroleum and Minerals under group project Nos. RG1217-1, RG1217-2, RG1214-1, and RG1214-2.

PY - 2014/8

Y1 - 2014/8

N2 - We perform modulational instability analysis of the Peregrine soliton. The eigensystem of the linearized perturbations results in time-dependent gain curve. The instantaneous stability of the Peregrine soliton is studied at different times and in terms of modulated spacial width. A correlation between the most unstable eigenmode and the time evolution of the Peregrine soliton is established. Our analysis explains the bifurcation of the Peregrine soliton into Ma breathers and the generation of shock waves. The theoretical approach and numerical procedure followed here may be applied to any other localized solution with nontrivial time dependence.

AB - We perform modulational instability analysis of the Peregrine soliton. The eigensystem of the linearized perturbations results in time-dependent gain curve. The instantaneous stability of the Peregrine soliton is studied at different times and in terms of modulated spacial width. A correlation between the most unstable eigenmode and the time evolution of the Peregrine soliton is established. Our analysis explains the bifurcation of the Peregrine soliton into Ma breathers and the generation of shock waves. The theoretical approach and numerical procedure followed here may be applied to any other localized solution with nontrivial time dependence.

KW - Modulational instability

KW - Peregrine

UR - https://www.scopus.com/pages/publications/84894348585

U2 - 10.1016/j.cnsns.2014.01.002

DO - 10.1016/j.cnsns.2014.01.002

M3 - Article

AN - SCOPUS:84894348585

SN - 1007-5704

VL - 19

SP - 2706

EP - 2714

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 8

ER -

Modulational instability analysis of the Peregrine soliton

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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