Derivation of the NLS breather solutions using displaced phase-amplitude variables

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Abstract

Breather solutions of the nonlinear Schrödinger equation are derived in this paper: the Soliton on Finite Background, the Ma breather and the rational breather. A special Ansatz of a displaced phase-amplitude equation with respect to a background is used as has been proposed by van Groesen et. al. (2006). Requiring the displaced phase to be temporally independent, has as consequence that the dynamics at each position is described by the motion of a nonlinear autonomous oscillator in a potential energy that depends on the phase and on the spatial phase change. The relation among the breather solutions is confirmed by explicit expressions, and illustrated with the amplitude amplification factor. Additionally, the corresponding physical wave field is also studied and wavefront dislocation together with phase singularity at vanishing amplitude are observed in all three cases.
Original languageUndefined
Title of host publicationProceedings of the 5th SEAMS-GMU International Conference on Mathematics and its Applications 2007, 24-27 July 2007, Yogyakarta,
Place of PublicationYogyakarta
PublisherUniversitas Gadjah Maja
Pages357-368
Number of pages12
ISBN (Print)978-979-95118-9-8
Publication statusPublished - 2008

Publication series

Name
PublisherUniversitas Gadjah Maja

Keywords

  • EWI-15081
  • METIS-255887
  • IR-65391

Cite this

Karjanto, N., & van Groesen, E. W. C. (2008). Derivation of the NLS breather solutions using displaced phase-amplitude variables. In Proceedings of the 5th SEAMS-GMU International Conference on Mathematics and its Applications 2007, 24-27 July 2007, Yogyakarta, (pp. 357-368). Yogyakarta: Universitas Gadjah Maja.
Karjanto, N. ; van Groesen, Embrecht W.C. / Derivation of the NLS breather solutions using displaced phase-amplitude variables. Proceedings of the 5th SEAMS-GMU International Conference on Mathematics and its Applications 2007, 24-27 July 2007, Yogyakarta,. Yogyakarta : Universitas Gadjah Maja, 2008. pp. 357-368
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title = "Derivation of the NLS breather solutions using displaced phase-amplitude variables",
abstract = "Breather solutions of the nonlinear Schr{\"o}dinger equation are derived in this paper: the Soliton on Finite Background, the Ma breather and the rational breather. A special Ansatz of a displaced phase-amplitude equation with respect to a background is used as has been proposed by van Groesen et. al. (2006). Requiring the displaced phase to be temporally independent, has as consequence that the dynamics at each position is described by the motion of a nonlinear autonomous oscillator in a potential energy that depends on the phase and on the spatial phase change. The relation among the breather solutions is confirmed by explicit expressions, and illustrated with the amplitude amplification factor. Additionally, the corresponding physical wave field is also studied and wavefront dislocation together with phase singularity at vanishing amplitude are observed in all three cases.",
keywords = "EWI-15081, METIS-255887, IR-65391",
author = "N. Karjanto and {van Groesen}, {Embrecht W.C.}",
year = "2008",
language = "Undefined",
isbn = "978-979-95118-9-8",
publisher = "Universitas Gadjah Maja",
pages = "357--368",
booktitle = "Proceedings of the 5th SEAMS-GMU International Conference on Mathematics and its Applications 2007, 24-27 July 2007, Yogyakarta,",

}

Karjanto, N & van Groesen, EWC 2008, Derivation of the NLS breather solutions using displaced phase-amplitude variables. in Proceedings of the 5th SEAMS-GMU International Conference on Mathematics and its Applications 2007, 24-27 July 2007, Yogyakarta,. Universitas Gadjah Maja, Yogyakarta, pp. 357-368.

Derivation of the NLS breather solutions using displaced phase-amplitude variables. / Karjanto, N.; van Groesen, Embrecht W.C.

Proceedings of the 5th SEAMS-GMU International Conference on Mathematics and its Applications 2007, 24-27 July 2007, Yogyakarta,. Yogyakarta : Universitas Gadjah Maja, 2008. p. 357-368.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

TY - GEN

T1 - Derivation of the NLS breather solutions using displaced phase-amplitude variables

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AU - van Groesen, Embrecht W.C.

PY - 2008

Y1 - 2008

N2 - Breather solutions of the nonlinear Schrödinger equation are derived in this paper: the Soliton on Finite Background, the Ma breather and the rational breather. A special Ansatz of a displaced phase-amplitude equation with respect to a background is used as has been proposed by van Groesen et. al. (2006). Requiring the displaced phase to be temporally independent, has as consequence that the dynamics at each position is described by the motion of a nonlinear autonomous oscillator in a potential energy that depends on the phase and on the spatial phase change. The relation among the breather solutions is confirmed by explicit expressions, and illustrated with the amplitude amplification factor. Additionally, the corresponding physical wave field is also studied and wavefront dislocation together with phase singularity at vanishing amplitude are observed in all three cases.

AB - Breather solutions of the nonlinear Schrödinger equation are derived in this paper: the Soliton on Finite Background, the Ma breather and the rational breather. A special Ansatz of a displaced phase-amplitude equation with respect to a background is used as has been proposed by van Groesen et. al. (2006). Requiring the displaced phase to be temporally independent, has as consequence that the dynamics at each position is described by the motion of a nonlinear autonomous oscillator in a potential energy that depends on the phase and on the spatial phase change. The relation among the breather solutions is confirmed by explicit expressions, and illustrated with the amplitude amplification factor. Additionally, the corresponding physical wave field is also studied and wavefront dislocation together with phase singularity at vanishing amplitude are observed in all three cases.

KW - EWI-15081

KW - METIS-255887

KW - IR-65391

M3 - Conference contribution

SN - 978-979-95118-9-8

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EP - 368

BT - Proceedings of the 5th SEAMS-GMU International Conference on Mathematics and its Applications 2007, 24-27 July 2007, Yogyakarta,

PB - Universitas Gadjah Maja

CY - Yogyakarta

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Karjanto N, van Groesen EWC. Derivation of the NLS breather solutions using displaced phase-amplitude variables. In Proceedings of the 5th SEAMS-GMU International Conference on Mathematics and its Applications 2007, 24-27 July 2007, Yogyakarta,. Yogyakarta: Universitas Gadjah Maja. 2008. p. 357-368