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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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Інститут математики НАН України
2008
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/149028 |
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irk-123456789-1490282019-02-20T01:28:48Z Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation Parkes, E.J. 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. 2008 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149028 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Parkes, E.J. |
| spellingShingle |
Parkes, E.J. Periodic and Solitary Travelling-Wave Solutions of an Extended Reduced Ostrovsky Equation Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Parkes, E.J. |
| author_sort |
Parkes, E.J. |
| title |
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_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_sort |
periodic and solitary travelling-wave solutions of an extended reduced ostrovsky equation |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149028 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT parkesej periodicandsolitarytravellingwavesolutionsofanextendedreducedostrovskyequation |
| first_indexed |
2023-05-20T17:32:01Z |
| last_indexed |
2023-05-20T17:32:01Z |
| _version_ |
1796153501131210752 |