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


Karjanto, N. and Groesen, E. van (2008) Derivation of the NLS breather solutions using displaced phase-amplitude variables. In: 5th SEAMS-GMU International Conference on Mathematics and its Applications 2007, 24-27 July 2007, Yogyakarta, Indonesia (pp. pp. 357-368).

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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.
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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