Exact solutions to the four Goldstone modes around a dark soliton of the nonlinear Schroedinger equation
arXiv:1102.0587 · doi:10.1088/1751-8113/44/13/135206
Abstract
This article is concerned with the linearisation around a dark soliton solution of the nonlinear Schrödinger 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.
14 pages, 3 figures, submitted to Journal of Physics A
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