Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach
Using the multiple scales method, the interaction between two bright and one dark solitons is studied. Provided that a long wave-short wave resonance condition is satisfied, the two-component Zakharov-Yajima-Oikawa (ZYO) completely integrable system is obtained. By using a Madelung fluid description...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146858 |
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| Cite this: | Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach / A. Visinescu, D. Grecu, R. Fedele, S. De Nicola // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 35 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862717595526889472 |
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| author | Visinescu, A. Grecu, D. Fedele, R. De Nicola, S. |
| author_facet | Visinescu, A. Grecu, D. Fedele, R. De Nicola, S. |
| citation_txt | Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach / A. Visinescu, D. Grecu, R. Fedele, S. De Nicola // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 35 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Using the multiple scales method, the interaction between two bright and one dark solitons is studied. Provided that a long wave-short wave resonance condition is satisfied, the two-component Zakharov-Yajima-Oikawa (ZYO) completely integrable system is obtained. By using a Madelung fluid description, the one-soliton solutions of the corresponding ZYO system are determined. Furthermore, a discussion on the interaction between one bright and two dark solitons is presented. In particular, this problem is reduced to solve a one-component ZYO system in the resonance conditions.
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| first_indexed | 2025-12-07T18:11:27Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146858 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:11:27Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
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| spelling | Visinescu, A. Grecu, D. Fedele, R. De Nicola, S. 2019-02-11T17:23:53Z 2019-02-11T17:23:53Z 2011 Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach / A. Visinescu, D. Grecu, R. Fedele, S. De Nicola // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 35 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35Q55; 37K10; 45G15 DOI:10.3842/SIGMA.2011.041 https://nasplib.isofts.kiev.ua/handle/123456789/146858 Using the multiple scales method, the interaction between two bright and one dark solitons is studied. Provided that a long wave-short wave resonance condition is satisfied, the two-component Zakharov-Yajima-Oikawa (ZYO) completely integrable system is obtained. By using a Madelung fluid description, the one-soliton solutions of the corresponding ZYO system are determined. Furthermore, a discussion on the interaction between one bright and two dark solitons is presented. In particular, this problem is reduced to solve a one-component ZYO system in the resonance conditions. This paper is a contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)” (June 14–18, 2010, Varna, Bulgaria). The full collection is available at http://www.emis.de/journals/SIGMA/SIDE-9.html.
 Support through CNCSIS program IDEI-571/2008 is acknowledged. The authors are indebted
 to an anonymous referee for drawing their attention to the paper [26]. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach Article published earlier |
| spellingShingle | Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach Visinescu, A. Grecu, D. Fedele, R. De Nicola, S. |
| title | Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach |
| title_full | Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach |
| title_fullStr | Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach |
| title_full_unstemmed | Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach |
| title_short | Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach |
| title_sort | periodic and solitary wave solutions of two component zakharov-yajima-oikawa system, using madelung's approach |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146858 |
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