skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Exact Bogoliubov-de Gennes solutions for gray-soliton backgrounds

Abstract

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.

Authors:
;  [1]
  1. Physics Department and State Research Center OPTIMAS, University of Kaiserslautern, Erwin-Schroedinger-Strasse 46, D-67663 Kaiserslautern (Germany)
Publication Date:
OSTI Identifier:
22051352
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; AMPLITUDES; BOGOLYUBOV TRANSFORMATION; EXACT SOLUTIONS; EXCITATION; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; SCHROEDINGER EQUATION; SOLITONS

Citation Formats

Walczak, P. B., and Anglin, J. R.. Exact Bogoliubov-de Gennes solutions for gray-soliton backgrounds. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.013611.
Walczak, P. B., & Anglin, J. R.. Exact Bogoliubov-de Gennes solutions for gray-soliton backgrounds. United States. doi:10.1103/PHYSREVA.84.013611.
Walczak, P. B., and Anglin, J. R.. Fri . "Exact Bogoliubov-de Gennes solutions for gray-soliton backgrounds". United States. doi:10.1103/PHYSREVA.84.013611.
@article{osti_22051352,
title = {Exact Bogoliubov-de Gennes solutions for gray-soliton backgrounds},
author = {Walczak, P. B. and Anglin, J. R.},
abstractNote = {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.},
doi = {10.1103/PHYSREVA.84.013611},
journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 84,
place = {United States},
year = {2011},
month = {7}
}