Abstract
A constructive method is given for the integration of the overdetermined system of nonlinear d'Alembert wave and eikonal equations □u = F1(u), uxµuxµ = F2(u). With the aid of this method one obtains a complete analytic description of the set of the smooth solutions of this system.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 11, pp. 1471–1487, November, 1991.
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Fushchich, V.I., Zhdanov, R.Z. & Revenko, I.V. General solutions of the nonlinear wave equation and of the eikonal equation. Ukr Math J 43, 1364–1379 (1991). https://doi.org/10.1007/BF01067274
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DOI: https://doi.org/10.1007/BF01067274