### Abstract

Original language | Undefined |
---|---|

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

Place of Publication | Yogyakarta |

Publisher | Universitas Gadjah Maja |

Pages | 357-368 |

Number of pages | 12 |

ISBN (Print) | 978-979-95118-9-8 |

Publication status | Published - 2008 |

### Publication series

Name | |
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Publisher | Universitas Gadjah Maja |

### Keywords

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

### Cite this

*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.

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

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

AU - Karjanto, N.

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

SP - 357

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

ER -