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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2013
Main Author: Miškinis, P.
Format: Article
Language:English
Published: Інститут математики НАН України 2013
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149222
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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
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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.
first_indexed 2025-12-07T20:46:33Z
format Article
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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
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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