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:arXiv.org 2013-02
Main Author: Miskinis, Paulius
Format: Article
Language:English
Subjects:
Burgers equation
Exact solutions
Linear equations
Nonlinearity
Quadratic equations
Transformations
Traveling waves
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.
ISSN:2331-8422
DOI:10.48550/arxiv.1302.6000