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A Generalization of the Hopf-Cole Transformation
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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A Generalization of the Hopf-Cole Transformation
Інший ID:
2010 Mathematics Subject Classification: 26A33; 35K55; 45K05
DOI: http://dx.doi.org/10.3842/SIGMA.2013.016
DOI: http://dx.doi.org/10.3842/SIGMA.2013.016
Посилання:
A Generalization of the Hopf-Cole Transformation / P. Miškinis // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 43 назв. — англ.
Підтримка:
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).
Дата:
2013
Переглядів:
623
Завантажень:
243
Анотація:
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.
