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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Bibliographic Details
Published in:Symmetry, integrability and geometry, methods and applications integrability and geometry, methods and applications, 2013-01, Vol.9, p.016
Main Author: Miskinis, Paulius
Format: Article
Language:English
Subjects:
Burgers equation
diffusion equation
nonlinearity
nonlocality
Online Access:Get full text
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Summary: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. [ProQuest: [...] denotes formulae omitted.]
ISSN:1815-0659
1815-0659
DOI:10.3842/SIGMA.2013.016