Soliton Condensates for the Focusing Nonlinear Schrödinger Equation: a Non-Bound State Case
In this paper, we study the spectral theory of soliton condensates - a special limit of soliton gases - for the focusing NLS (fNLS). In particular, we analyze the kinetic equation for the fNLS circular condensate, which represents the first example of an explicitly solvable fNLS condensate with nont...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212350 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Soliton Condensates for the Focusing Nonlinear Schrödinger Equation: a Non-Bound State Case. Alexander Tovbis and Fudong Wang. SIGMA 20 (2024), 070, 26 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862660966435520512 |
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| author | Tovbis, Alexander Wang, Fudong |
| author_facet | Tovbis, Alexander Wang, Fudong |
| citation_txt | Soliton Condensates for the Focusing Nonlinear Schrödinger Equation: a Non-Bound State Case. Alexander Tovbis and Fudong Wang. SIGMA 20 (2024), 070, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we study the spectral theory of soliton condensates - a special limit of soliton gases - for the focusing NLS (fNLS). In particular, we analyze the kinetic equation for the fNLS circular condensate, which represents the first example of an explicitly solvable fNLS condensate with nontrivial large-scale space-time dynamics. Solution of the kinetic equation was obtained by reducing it to Whitham-type equations for the endpoints of spectral arcs. We also study the rarefaction and dispersive shock waves for circular condensates, as well as calculate the corresponding average conserved quantities and the kurtosis. We want to note that one of the main objects of the spectral theory - the nonlinear dispersion relations - is introduced in the paper as some special large genus (thermodynamic) limit of the Riemann bilinear identities that involve the quasimomentum and the quasienergy meromorphic differentials.
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| first_indexed | 2026-03-16T04:01:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212350 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T04:01:57Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Tovbis, Alexander Wang, Fudong 2026-02-05T09:55:43Z 2024 Soliton Condensates for the Focusing Nonlinear Schrödinger Equation: a Non-Bound State Case. Alexander Tovbis and Fudong Wang. SIGMA 20 (2024), 070, 26 pages 1815-0659 2020 Mathematics Subject Classification: 37K40; 35P30; 37K10 arXiv:2312.16406 https://nasplib.isofts.kiev.ua/handle/123456789/212350 https://doi.org/10.3842/SIGMA.2024.070 In this paper, we study the spectral theory of soliton condensates - a special limit of soliton gases - for the focusing NLS (fNLS). In particular, we analyze the kinetic equation for the fNLS circular condensate, which represents the first example of an explicitly solvable fNLS condensate with nontrivial large-scale space-time dynamics. Solution of the kinetic equation was obtained by reducing it to Whitham-type equations for the endpoints of spectral arcs. We also study the rarefaction and dispersive shock waves for circular condensates, as well as calculate the corresponding average conserved quantities and the kurtosis. We want to note that one of the main objects of the spectral theory - the nonlinear dispersion relations - is introduced in the paper as some special large genus (thermodynamic) limit of the Riemann bilinear identities that involve the quasimomentum and the quasienergy meromorphic differentials. The authors would also like to thank the anonymous referees for their useful suggestions and comments. FudongWang is supported by the Guangdong Basic and Applied Basic Research Foundation B24030004J. The work of Alexander Tovbis is supported in part by NSF Grant DMS-2009647. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Soliton Condensates for the Focusing Nonlinear Schrödinger Equation: a Non-Bound State Case Article published earlier |
| spellingShingle | Soliton Condensates for the Focusing Nonlinear Schrödinger Equation: a Non-Bound State Case Tovbis, Alexander Wang, Fudong |
| title | Soliton Condensates for the Focusing Nonlinear Schrödinger Equation: a Non-Bound State Case |
| title_full | Soliton Condensates for the Focusing Nonlinear Schrödinger Equation: a Non-Bound State Case |
| title_fullStr | Soliton Condensates for the Focusing Nonlinear Schrödinger Equation: a Non-Bound State Case |
| title_full_unstemmed | Soliton Condensates for the Focusing Nonlinear Schrödinger Equation: a Non-Bound State Case |
| title_short | Soliton Condensates for the Focusing Nonlinear Schrödinger Equation: a Non-Bound State Case |
| title_sort | soliton condensates for the focusing nonlinear schrödinger equation: a non-bound state case |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212350 |
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