### 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 language | Undefined |
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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

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.