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arXiv · 1102.0587

Exact solutions to the four Goldstone modes around a dark soliton of the nonlinear Schroedinger equation

Andrew Sykes
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Abstract

This article is concerned with the linearisation around a dark soliton solution of the nonlinear Schr\"odinger equation. Crucially, we present analytic expressions for the four linearly-independent zero eigenvalue solutions (also known as Goldstone modes) to the linearised problem. These solutions are then used to construct a Greens matrix which gives the first-order spatial response due to some perturbation. Finally we apply this Greens matrix to find the correction to the dark-soliton wavefunction of a Bose-Einstein condensate in the presence of fluctuations.

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Andrew Sykes. 2011-02-02. Exact solutions to the four Goldstone modes around a dark soliton of the nonlinear Schroedinger equation. https://doi.org/10.1088/1751-8113/44/13/135206

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