2013/09/05 by Stan Alama, Lia Bronsard, Andres Contreras +2 · 30 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Class (philosophy) #Cold Atom Physics and Bose-Einstein Condensates #Domain (mathematical analysis) #Domain wall (magnetism) #Energy (signal processing) #Frequency domain #Line (geometry) #Nonlinear Photonic Systems #Nonlinear system #Operator (biology) #Stability (learning theory) #math.AP
paper · pdf · doi:10.1007/s00205-014-0789-y
published in Archive for Rational Mechanics and Analysis 215(2), 579-610 (Springer Science+Business Media)
arxiv created 2013/09/05 · openalex publication_date 2014/09/04 · arxiv updated 2015/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A thorough study of domain wall solutions in coupled Gross-Pitaevskii equations on the real line is carried out including existence of these solutions; their spectral and nonlinear stability; their persistence and stability under a small localized potential. The proof of existence is variational and is presented in a general framework: we show that the domain wall solutions are energy minimizing within a class of vector-valued functions with nontrivial conditions at infinity. The admissible energy functionals include those corresponding to coupled Gross--Pitaevskii equations, arising in modeling of Bose-Einstein condensates. The results on spectral and nonlinear stability follow from properties of the linearized operator about the domain wall. The methods apply to many systems of interest and integrability is not germane to our analysis. Finally, sufficient conditions for persistence and stability of domain wall solutions are obtained to show that stable pinning occurs near maxima of the potential, thus giving rigorous justification to earlier results in the physics literature.