Exact Bogoliubov–de Gennes solutions for gray-soliton backgrounds

We derive and discuss the complete set of exact solutions to the one-dimensional Bogoliubov-de Gennes equations for small-amplitude excitations around general gray-soliton solutions to the cubic nonlinear Schroedinger equation. Our results extend the previously known case of the motionless dark-soli...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2011-07, Vol.84 (1), Article 013611
Main Authors: Walczak, P. B., Anglin, J. R.
Format: Article
Language:English
Subjects:
AMPLITUDES
BOGOLYUBOV TRANSFORMATION
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
EXACT SOLUTIONS
EXCITATION
MATHEMATICAL METHODS AND COMPUTING
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
SCHROEDINGER EQUATION
SOLITONS
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Summary:We derive and discuss the complete set of exact solutions to the one-dimensional Bogoliubov-de Gennes equations for small-amplitude excitations around general gray-soliton solutions to the cubic nonlinear Schroedinger equation. Our results extend the previously known case of the motionless dark-soliton background. We derive our nonzero-frequency solutions using a variant of the factorization method for Schroedinger equations with reflectionless potentials. We also discuss the zero-mode solutions at length.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.84.013611