Abstract
New results on group theoretical aspects of the Huygens principle are presented. An extension of Darboux-Lagnese-Stellmacher’s transformation to the wave equations in spaces with non-trivial conformai group is considered. Fundamental solutions of selected Huygens’ equations are constructed by using a new adaptation of the group theoretic technique for distributions. It is observed that the hierarchy of Huygens’ equations is closely related to that of rational solutions for higher Korteweg-de Vries equations.
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Berest, Y.Y., Ibragimov, N.H., Oganesyan, A.O. (1993). Conformal Invariance, Huygens Principle and Fundamental Solutions for Scalar Second Order Hyperbolic Equations. In: Ibragimov, N.H., Torrisi, M., Valenti, A. (eds) Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2050-0_6
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