Exact Bogoliubov-de Gennes Solutions for Grey Soliton Backgrounds

2011/04/05 by Philip B. Walczak, Walczak, Philip B., James R. Anglin +1 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.1104.0886

arxiv created 2011/04/05 · openalex publication_date 2011/04/05 · arxiv updated 2011/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 grey soliton solutions to the cubic nonlinear Schrödinger equation. Our results extend the previously known case of the motionless dark soliton background. We derive our non-zero frequency solutions using a variant of the factorization method for Schrödinger equations with reflectionless potentials. We also discuss the zero mode solutions at length.

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