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SIGMA, 2005, Volume 1, 027, 11 pp.
(Mi sigma27)
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This article is cited in 11 scientific papers (total in 11 papers)
Integrable Anisotropic Evolution Equations on a Sphere
Anatoly G. Meshkov, Maxim Ju. Balakhnev
Orel State University, 95 Komsomol'skaya Str., Orel, 302026 Russia
Abstract:
V.V. Sokolov's modifying symmetry approach is applied to anisotropic evolution equations of the third order on the $n$-dimensional sphere. The main result is a complete classification of such equations. Auto-Bäcklund transformations are also found for all equations.
Keywords:
evolution equation; equation on a sphere; integrability; symmetry classification; anisotropy; conserved densities; Bäcklund transformations
DOI:
https://doi.org/10.3842/SIGMA.2005.027
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http://emis.mi.ras.ru/.../Paper027
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ArXiv:
nlin.SI/0512032
MSC: 35Q58; 35L65; 37K10; 37K35
Received: September 25, 2005; in final form December 9, 2005; Published online December 14, 2005
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Citation:
Anatoly G. Meshkov, Maxim Ju. Balakhnev, “Integrable Anisotropic Evolution Equations on a Sphere”, SIGMA, 1 (2005), 027, 11 pp.
Citation in format AMSBIB
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\by Anatoly G. Meshkov, Maxim Ju. Balakhnev
\paper Integrable Anisotropic Evolution Equations on a~Sphere
\jour SIGMA
\yr 2005
\vol 1
\papernumber 027
\totalpages 11
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http://mi.mathnet.ru/eng/sigma27 http://mi.mathnet.ru/eng/sigma/v1/p27
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
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A. G. Meshkov, “On symmetry classification of third order evolutionary systems of divergent type”, J. Math. Sci., 151:4 (2008), 3167–3181
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M. Yu. Balakhnev, “Superposition formulas for integrable vector evolution equations”, Theoret. and Math. Phys., 154:2 (2008), 220–226
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Anatoly G.G. Meshkov, Maxim Ju. Balakhnev, “Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions”, SIGMA, 4 (2008), 018, 29 pp.
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Balakhnev, MJ, “On a classification of integrable vectorial evolutionary equations”, Journal of Nonlinear Mathematical Physics, 15:2 (2008), 212
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Balakhnev M.J., “Superposition formulas for integrable vector evolutionary equations on a sphere”, Journal of Nonlinear Mathematical Physics, 15:1 (2008), 104–116
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M. Yu. Balakhnev, A. G. Meshkov, “Integrable vector evolution equations admitting zeroth-order conserved densities”, Theoret. and Math. Phys., 164:2 (2010), 1002–1007
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M. Yu. Balakhnev, “First-Order Differential Substitutions for Equations Integrable on $\mathbb S^n$”, Math. Notes, 89:2 (2011), 184–193
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Balakhnev M.J., “New examples of the auto-Backlund transformations and nonlinear superposition formulas for vector evolution systems”, Phys Lett A, 375:3 (2011), 529–536
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A. G. Meshkov, V. V. Sokolov, “Integriruemye evolyutsionnye uravneniya s postoyannoi separantoi”, Ufimsk. matem. zhurn., 4:3 (2012), 104–154
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M. Yu. Balakhnev, “Integrable Vector Isotropic Equations Admitting Differential Substitutions of First Order”, Math. Notes, 94:3 (2013), 307–313
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Meshkov A., Sokolov V., “Vector Hyperbolic Equations on the Sphere Possessing Integrable Third-Order Symmetries”, Lett. Math. Phys., 104:3 (2014), 341–360
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