Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation
Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the reduced Ostrovsky equation. It is shown how the nature of the w...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2008 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2008
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149028 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation / E.J. Parkes // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 24 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862708846535901184 |
|---|---|
| author | Parkes, E.J. |
| author_facet | Parkes, E.J. |
| citation_txt | Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation / E.J. Parkes // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the reduced Ostrovsky equation. It is shown how the nature of the waves may be categorized in a simple way by considering the value of a certain single combination of constant parameters. The periodic waves may be smooth humps, cuspons, loops or parabolic corner waves. The latter are shown to be the maximum-amplitude limit of a one-parameter family of periodic smooth-hump waves. The solitary waves may be a smooth hump, a cuspon, a loop or a parabolic wave with compact support. All the solutions are expressed in parametric form. Only in one circumstance can the variable parameter be eliminated to give a solution in explicit form. In this case the resulting waves are either a solitary parabolic wave with compact support or the corresponding periodic corner waves.
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| first_indexed | 2025-12-07T17:13:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149028 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:13:37Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Parkes, E.J. 2019-02-19T13:09:06Z 2019-02-19T13:09:06Z 2008 Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation / E.J. Parkes // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 24 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35Q58; 35Q53: 35C05 https://nasplib.isofts.kiev.ua/handle/123456789/149028 Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the reduced Ostrovsky equation. It is shown how the nature of the waves may be categorized in a simple way by considering the value of a certain single combination of constant parameters. The periodic waves may be smooth humps, cuspons, loops or parabolic corner waves. The latter are shown to be the maximum-amplitude limit of a one-parameter family of periodic smooth-hump waves. The solitary waves may be a smooth hump, a cuspon, a loop or a parabolic wave with compact support. All the solutions are expressed in parametric form. Only in one circumstance can the variable parameter be eliminated to give a solution in explicit form. In this case the resulting waves are either a solitary parabolic wave with compact support or the corresponding periodic corner waves. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). The author thanks the referees for some perceptive comments and for recommending some additional references. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation Article published earlier |
| spellingShingle | Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation Parkes, E.J. |
| title | Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation |
| title_full | Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation |
| title_fullStr | Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation |
| title_full_unstemmed | Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation |
| title_short | Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation |
| title_sort | periodic and solitary travelling-wave solutions of an extended reduced ostrovsky equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149028 |
| work_keys_str_mv | AT parkesej periodicandsolitarytravellingwavesolutionsofanextendedreducedostrovskyequation |