Separation of variables in the two-dimensional wave equation with potential
The paper is devoted to solution of a problem of separation of variables in the wave equation utt−uxx+V(x)u=0. We give a complete classification of potentials V(x) for which this equation admits a nontrivial separation of variables. Furthermore, we obtain all coordinate systems that provide separabi...
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| Published in: | Український математичний журнал |
|---|---|
| Date: | 1994 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
1994
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/156751 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Separation of variables in the two-dimensional wave equation with potential / R.Z. Zhdanov, I.V. Revenko, W.I. Fushchych // Український математичний журнал. — 1994. — Т. 46, № 10. — С. 1343–1361. — Бібліогр.: 19 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859777361517477888 |
|---|---|
| author | Zhdanov, R.Z. Revenko, I.V. Fushchych, W.I. |
| author_facet | Zhdanov, R.Z. Revenko, I.V. Fushchych, W.I. |
| citation_txt | Separation of variables in the two-dimensional wave equation with potential / R.Z. Zhdanov, I.V. Revenko, W.I. Fushchych // Український математичний журнал. — 1994. — Т. 46, № 10. — С. 1343–1361. — Бібліогр.: 19 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний журнал |
| description | The paper is devoted to solution of a problem of separation of variables in the wave equation utt−uxx+V(x)u=0. We give a complete classification of potentials V(x) for which this equation admits a nontrivial separation of variables. Furthermore, we obtain all coordinate systems that provide separability of the equation considered.
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| first_indexed | 2025-12-02T08:44:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156751 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1027-3190 |
| language | English |
| last_indexed | 2025-12-02T08:44:45Z |
| publishDate | 1994 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Zhdanov, R.Z. Revenko, I.V. Fushchych, W.I. 2019-06-18T20:06:03Z 2019-06-18T20:06:03Z 1994 Separation of variables in the two-dimensional wave equation with potential / R.Z. Zhdanov, I.V. Revenko, W.I. Fushchych // Український математичний журнал. — 1994. — Т. 46, № 10. — С. 1343–1361. — Бібліогр.: 19 назв. — англ. 1027-3190 https://nasplib.isofts.kiev.ua/handle/123456789/156751 517.944:519.46 The paper is devoted to solution of a problem of separation of variables in the wave equation utt−uxx+V(x)u=0. We give a complete classification of potentials V(x) for which this equation admits a nontrivial separation of variables. Furthermore, we obtain all coordinate systems that provide separability of the equation considered. en Інститут математики НАН України Український математичний журнал Статті Separation of variables in the two-dimensional wave equation with potential Розділення змінних у двовимірному хвильовому рівнянні з потенціалом Article published earlier |
| spellingShingle | Separation of variables in the two-dimensional wave equation with potential Zhdanov, R.Z. Revenko, I.V. Fushchych, W.I. Статті |
| title | Separation of variables in the two-dimensional wave equation with potential |
| title_alt | Розділення змінних у двовимірному хвильовому рівнянні з потенціалом |
| title_full | Separation of variables in the two-dimensional wave equation with potential |
| title_fullStr | Separation of variables in the two-dimensional wave equation with potential |
| title_full_unstemmed | Separation of variables in the two-dimensional wave equation with potential |
| title_short | Separation of variables in the two-dimensional wave equation with potential |
| title_sort | separation of variables in the two-dimensional wave equation with potential |
| topic | Статті |
| topic_facet | Статті |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156751 |
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