Initial Value Problems for Integrable Systems on a Semi-Strip
Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix solutions of the defocusing nonlinear Schrödinger equation wi...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147424 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Initial Value Problems for Integrable Systems on a Semi-Strip / A.L. Sakhnovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 60 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862729492765605888 |
|---|---|
| author | Sakhnovich, A.L. |
| author_facet | Sakhnovich, A.L. |
| citation_txt | Initial Value Problems for Integrable Systems on a Semi-Strip / A.L. Sakhnovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 60 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix solutions of the defocusing nonlinear Schrödinger equation with quasi-analytic boundary conditions is dealt with. (The result is new even for a scalar nonlinear Schrödinger equation.) Next, a special case of the nonlinear optics (N-wave) equation is considered.
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| first_indexed | 2025-12-07T19:15:03Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147424 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:15:03Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sakhnovich, A.L. 2019-02-14T18:19:38Z 2019-02-14T18:19:38Z 2016 Initial Value Problems for Integrable Systems on a Semi-Strip / A.L. Sakhnovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 60 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35Q55; 35Q60; 34B20; 35A02 DOI:10.3842/SIGMA.2016.001 https://nasplib.isofts.kiev.ua/handle/123456789/147424 Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix solutions of the defocusing nonlinear Schrödinger equation with quasi-analytic boundary conditions is dealt with. (The result is new even for a scalar nonlinear Schrödinger equation.) Next, a special case of the nonlinear optics (N-wave) equation is considered. This research was supported by the Austrian Science Fund (FWF) under Grant No. P24301.
 The author is grateful to A. Rainer for a helpful discussion on quasi-analytic functions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Initial Value Problems for Integrable Systems on a Semi-Strip Article published earlier |
| spellingShingle | Initial Value Problems for Integrable Systems on a Semi-Strip Sakhnovich, A.L. |
| title | Initial Value Problems for Integrable Systems on a Semi-Strip |
| title_full | Initial Value Problems for Integrable Systems on a Semi-Strip |
| title_fullStr | Initial Value Problems for Integrable Systems on a Semi-Strip |
| title_full_unstemmed | Initial Value Problems for Integrable Systems on a Semi-Strip |
| title_short | Initial Value Problems for Integrable Systems on a Semi-Strip |
| title_sort | initial value problems for integrable systems on a semi-strip |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147424 |
| work_keys_str_mv | AT sakhnovichal initialvalueproblemsforintegrablesystemsonasemistrip |