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Symmetry, Integrability and Geometry: Methods and Applications, 2013, Volume 9, 016, 19 pp.
DOI: https://doi.org/10.3842/SIGMA.2013.016 (Mi sigma799) 		 
This article is cited in 5 scientific papers (total in 5 papers)

A Generalization of the Hopf–Cole Transformation

Paulius Miškinis

Department of Physics, Faculty of Fundamental Sciences, Vilnius Gediminas Technical University, Saulėtekio Ave 11, LT-10223, Vilnius-40, Lithuania
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DOI: https://doi.org/10.3842/SIGMA.2013.016
Abstract: 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.
Keywords: nonlocality; nonlinearity; diffusion equation; Burgers equation.
Received: June 4, 2012; in final form February 17, 2013; Published online February 25, 2013
Bibliographic databases:
Document Type: Article
MSC: 26A33; 35K55; 45K05
Language: English
Citation: Paulius Miškinis, “A Generalization of the Hopf–Cole Transformation”, SIGMA, 9 (2013), 016, 19 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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