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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| Date: | 1994 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
1994
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| Series: | Український математичний журнал |
| Subjects: | |
| Online Access: | http://dspace.nbuv.gov.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| Summary: | 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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