We consider a generalized procedure of separation of variables in nonlinear hyperbolic-type equations and Korteweg–de-Vries-type equations. We construct a broad class of exact solutions of these equations that cannot be obtained by the Lie method and method of conditional symmetries.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 12, pp. 1598–1608, December, 2010.
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Barannyk, A.F., Barannyk, T.A. & Yuryk, I.I. Generalized separation of variables and exact solutions of nonlinear equations. Ukr Math J 62, 1852–1865 (2011). https://doi.org/10.1007/s11253-011-0475-2
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DOI: https://doi.org/10.1007/s11253-011-0475-2