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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Main Author:	Paulius Miškinis
Format:	Article
Language:	English
Published:	National Academy of Science of Ukraine 2013-02-01
Series:	Symmetry, Integrability and Geometry: Methods and Applications
Subjects:	nonlocality nonlinearity diffusion equation Burgers equation
Online Access:	http://dx.doi.org/10.3842/SIGMA.2013.016

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spelling	doaj-8b943cdc31c44c7c9d44358344984c7d2020-11-25T00:11:53ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592013-02-019016A Generalization of the Hopf-Cole TransformationPaulius MiškinisA 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.http://dx.doi.org/10.3842/SIGMA.2013.016nonlocalitynonlinearitydiffusion equationBurgers equation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Paulius Miškinis
spellingShingle	Paulius Miškinis A Generalization of the Hopf-Cole Transformation Symmetry, Integrability and Geometry: Methods and Applications nonlocality nonlinearity diffusion equation Burgers equation
author_facet	Paulius Miškinis
author_sort	Paulius Miškinis
title	A Generalization of the Hopf-Cole Transformation
title_short	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_sort	generalization of the hopf-cole transformation
publisher	National Academy of Science of Ukraine
series	Symmetry, Integrability and Geometry: Methods and Applications
issn	1815-0659
publishDate	2013-02-01
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.
topic	nonlocality nonlinearity diffusion equation Burgers equation
url	http://dx.doi.org/10.3842/SIGMA.2013.016
work_keys_str_mv	AT pauliusmiskinis ageneralizationofthehopfcoletransformation AT pauliusmiskinis generalizationofthehopfcoletransformation
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A Generalization of the Hopf-Cole Transformation

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