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Application of Group Analysis to Find the Function Riemann
Current Issue
Volume 3, 2015
Issue 5 (October)
Pages: 128-131   |   Vol. 3, No. 5, October 2015   |   Follow on         
Paper in PDF Downloads: 52   Since Sep. 8, 2015 Views: 1494   Since Sep. 8, 2015
Authors
[1]
Akimov Andrey, Department of Physics and Mathematics, Bashkir State University Sterlitamak Branch, Sterlitamak, Russia.
[2]
Rufina Abdullina, Department of Physics and Mathematics, Bashkir State University Sterlitamak Branch, Sterlitamak, Russia.
Abstract
This paper is of a synthetic nature, being a result of combining Riemann’s method for integrating second-order linear hyperbolic equations with Lie’s classification of such equations In paper for the hyperbolic equation was constructed the four-parameter group and with the help of the group was found the solution of the Cauchy problem by the Riemann method for a hyperbolic equation.
Keywords
Problem Cauchy, Riemann’s Function, Hyperbolic Equation, Group Analysis
Reference
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Akimov A. A., On uniqueness Morawetz problem for the Chaplygin equation, IJPAM, vol. 97, No. 3, (2014), 369-375.
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Akimov A. A., Some Properties and Applications of the Riemann-Hadamard Function of Darboux Problem for Telegraph Equation, American Research Journal of Mathematics, Volume 1, Issue 3, (2015), 9-15.
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[11]
Lerner, M.E., Qualitative Properties of the Riemann Function, Differ. Uravn., vol. 27, No. 12, (1991), 2106–2120.
[12]
Bitsadze, A. V., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Nauka, (1976).
[13]
N. H. Ibragimov. Group analysis of ordinary differential equations and the invariance principle in mathematical physics (for the 150th anniversary of Sophus Lie). Uspekhi Mat. Nauk, 47, No. 4:83–144, 1992. English transl., Russian Math. Surveys, 47:2 (1992), 89-156.
[14]
P. J. Olver. Applications of Lie groups to differential equations. Springer-Verlag, New York, 1986. 2nd ed., 1993.
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