Generalized separation of variables and exact solutions of nonlinear equations
We consider the generalized procedure of separation of variables of the nonlinear hyperbolic-type equations and the Korteweg - de Vries-type equations. We construct a wide class of exact solutions of these equations which cannot be obtained with the use of the S. Lie method and the method of conditional symmetries.
English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 12, pp 1852-1865.
Citation Example: Barannik A. F., Barannik A. F., Yuryk I. I. Generalized separation of variables and exact solutions of nonlinear equations // Ukr. Mat. Zh. - 2010. - 62, № 12. - pp. 1598 - 1609.