Solutions of Gross–Pitaevskii equation with periodic potential in dimension three
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- by Yu. Karpeshina, Seonguk Kim and R. Shterenberg
- St. Petersburg Math. J. 35 (2024), 153-169
- DOI: https://doi.org/10.1090/spmj/1798
- Published electronically: April 12, 2024
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Abstract:
Quasiperiodic solutions of the Gross–Pitaevskii equation with a periodic potential in dimension three are studied. It is proved that there is an extensive “nonresonant” set $\mathcal {G}\subset \mathbb {R}^3$ such that for every $\overrightarrow k\in \mathcal {G}$ there is a solution asymptotically close to a plane wave $Ae^{i\langle \overrightarrow {k},\overrightarrow {x}\rangle }$ as $|\overrightarrow k|\to \infty$, given $A$ is sufficiently small.References
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Bibliographic Information
- Yu. Karpeshina
- Affiliation: Department of Mathematics, Campbell Hall, University of Alabama at Birmingham, 1300 University Boulevard, Birmingham, Alabama 35294
- MR Author ID: 189810
- Email: karpeshi@uab.edu
- Seonguk Kim
- Affiliation: Division of Natural Science, Applied Science, and Mathematics, Defiance College, Defiance, 43512, Ohio
- ORCID: setImmediate$0.985030072435894$3
- Email: skim@defiance.edu
- R. Shterenberg
- Affiliation: Department of Mathematics, Campbell Hall, University of Alabama at Birmingham, 1300 University Boulevard, Birmingham, Alabama 35294
- Email: shterenb@uab.edu
- Received by editor(s): September 24, 2021
- Published electronically: April 12, 2024
- Additional Notes: Supported in part by NSF-grants DMS-1814664 (Y.K. and R.S)
- © Copyright 2024 American Mathematical Society
- Journal: St. Petersburg Math. J. 35 (2024), 153-169
- MSC (2020): Primary 35Q40
- DOI: https://doi.org/10.1090/spmj/1798
Dedicated: To the memory of S. N. Naboko