Generalized separation of variable for nonlinear equation utt=a(t)uxx+b(t)u2x+c(t)uutt=a(t)uxx+b(t)ux2+c(t)u
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We propose a generalized procedure of separation of variables for nonlinear equations and construct broad classes of exact solutions of these equations that cannot be obtained by the classical Lie method and the method of conditional symmetries.
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Barannyk, A. Generalized separation of variables for nonlinear equation utt=a(t)uxx+b(t)u2x+c(t)uutt=a(t)uxx+b(t)ux2+c(t)u / A. Barannyk, T. Barannyk, I. Yuryk // Symmetry and Integrability of Equations of Mathematical Physics : Abstracts of International Conference. – Kyiv, 2015. – P. 23.