Abstract
The Lie group theory and Leray’s form provide a covariant (i.e., independent of a coordinate system) method for the calculation of fundamental solutions for linear hyperbolic equations, and hence for the solution of Cauchy’s problem. Here, the method is illustrated by the classical wave equation.
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References
Ibragimov, N.H., (i) Primer of the group analysis, Moscow: Znanie, no. 8, 1989. Group analysis of ordinary differential equations and the invariance principle in mathematical physics (to the 150th anniversary of Sophus Lie), Uspekhi Mat. Nauk (1992). Engl. transl. in Russian Math. Surveys 47(4) (1992), 89–156. (iii) Small effects in physics hinted by the Lie group philosophy: Are they observable? I. From Galilean principle to heat diffusion, Proceedings of Int. Conf. on Modern Group Analysis V, Johannesburg, South Africa, January 16–22, 1994, published in Lie Groups and Their Applications, vol. 1(1), 1994, 113–123. (iv) Differential equations with distributions: Group theoretic treatment of fundamental solutions, Chapter 3 in CRC Handbook ofLie Group Analysis ofDifferential Equations, N.H. Ibragimov (ed.), vol. 3, Boca Raton, Florida: CRC Press 1996, 69 – 90.
Leray, J., Hyperbolic differential equations, Mimeographed, The Institute for Advanced Study, Princeton 1953. Published in Russian translation by Ibragimov, N.H, Moscow: Nauka 1984.
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Ibragimov, N.H. (2003). Covariant Method for Solution of Cauchy’s Problem Based on Lie Group Analysis and Leray’s form. In: de Gosson, M. (eds) Jean Leray ’99 Conference Proceedings. Mathematical Physics Studies, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2008-3_27
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DOI: https://doi.org/10.1007/978-94-017-2008-3_27
Publisher Name: Springer, Dordrecht
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