A Generalization of the Hopf-Cole Transformation
A generalization of the Hopf-Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is presented. The existence of the travelling wave solution and the i...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2013 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2013
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149222 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Generalization of the Hopf-Cole Transformation / P. Miškinis // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 43 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862746700650643456 |
|---|---|
| author | Miškinis, P. |
| author_facet | Miškinis, P. |
| citation_txt | A Generalization of the Hopf-Cole Transformation / P. Miškinis // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 43 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A generalization of the Hopf-Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is presented. The existence of the travelling wave solution and the interaction of nonlocal perturbation are considered. The nonlocal generalizations of the one-dimensional diffusion equation with quadratic nonlinearity and of the Burgers equation are analyzed.
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| first_indexed | 2025-12-07T20:46:33Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149222 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:46:33Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Miškinis, P. 2019-02-19T18:59:53Z 2019-02-19T18:59:53Z 2013 A Generalization of the Hopf-Cole Transformation / P. Miškinis // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 43 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 26A33; 35K55; 45K05 DOI: http://dx.doi.org/10.3842/SIGMA.2013.016 https://nasplib.isofts.kiev.ua/handle/123456789/149222 A generalization of the Hopf-Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is presented. The existence of the travelling wave solution and the interaction of nonlocal perturbation are considered. The nonlocal generalizations of the one-dimensional diffusion equation with quadratic nonlinearity and of the Burgers equation are analyzed. This paper is a contribution to the Special Issue “Geometrical Methods in Mathematical Physics”. The full
 collection is available at http://www.emis.de/journals/SIGMA/GMMP2012.html.
 The author would like to express his gratitude to Professors B.A. Dubrovin, M. Pavlov and
 L. Alaniya for the invitation and kind hospitality during the Conference “Geometrical Methods
 in Mathematical Physics” (Moscow State University, December 12–17, 2011). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Generalization of the Hopf-Cole Transformation Article published earlier |
| spellingShingle | A Generalization of the Hopf-Cole Transformation Miškinis, P. |
| title | A Generalization of the Hopf-Cole Transformation |
| title_full | A Generalization of the Hopf-Cole Transformation |
| title_fullStr | A Generalization of the Hopf-Cole Transformation |
| title_full_unstemmed | A Generalization of the Hopf-Cole Transformation |
| title_short | A Generalization of the Hopf-Cole Transformation |
| title_sort | generalization of the hopf-cole transformation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149222 |
| work_keys_str_mv | AT miskinisp ageneralizationofthehopfcoletransformation AT miskinisp generalizationofthehopfcoletransformation |