Anatoly F. Barannyk (Institute of Mathematics, Pomeranian University, Slupsk, Poland)
Tetyana A. Barannyk (Poltava National Pedagogical University named after Korolenko)
Ivan I. Yuryk (Ukrainian State University of Food Technologies, Kyiv)

Generalized separation of variables for nonlinear equation $u_{tt}=a(t)u_{xx}+b(t)u_x^2+c(t)u$

Abstract:
Systems of coordinate functions are defined, that allows to reduce the problem of obtaining exact solutions with generalized separation of variables to integrating of system of ODEs. The conditions of possibility to integrate the obtained systems of equations are found.