caa a22 4500 605515417 CHVBK 20210128100709.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00205-014-0789-y doi (NATIONALLICENCE)springer-10.1007/s00205-014-0789-y Domain Walls in the Coupled Gross-Pitaevskii Equations [Elektronische Daten] [Stan Alama, Lia Bronsard, Andres Contreras, Dmitry Pelinovsky] 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 minimizers 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. Springer-Verlag Berlin Heidelberg, 2014 Alama Stan Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, ON, Canada aut Bronsard Lia Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, ON, Canada aut Contreras Andres Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, ON, Canada aut Pelinovsky Dmitry Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, ON, Canada aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/2(2015-02-01), 579-610 0003-9527 215:2<579 2015 215 205 https://doi.org/10.1007/s00205-014-0789-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0789-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alama Stan Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, ON, Canada aut NATIONALLICENCE 700 1- Bronsard Lia Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, ON, Canada aut NATIONALLICENCE 700 1- Contreras Andres Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, ON, Canada aut NATIONALLICENCE 700 1- Pelinovsky Dmitry Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, ON, Canada aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/2(2015-02-01), 579-610 0003-9527 215:2<579 2015 215 205