Exact solutions to the four Goldstone modes around a dark soliton of the nonlinear Schrödinger equation
Abstract
This paper is concerned with the linearization 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 linearized problem. These solutions are then used to construct a Green matrix which gives the firstorder spatial response due to some perturbation. Finally, we apply this Green matrix to find the correction to the darksoliton wavefunction of a BoseEinstein condensate in the presence of fluctuations.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 April 2011
 DOI:
 10.1088/17518113/44/13/135206
 arXiv:
 arXiv:1102.0587
 Bibcode:
 2011JPhA...44m5206S
 Keywords:

 Condensed Matter  Quantum Gases;
 Mathematical Physics
 EPrint:
 14 pages, 3 figures, submitted to Journal of Physics A