Title | Construction of exact solutions to nonlinear equations of the hyperbolic type |
Publication Type | Journal Article |
Year of Publication | 2017 |
Authors | Barannyk, AF, Barannyk, TA, Yuryk, II |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2017.07.003 |
Issue | 7 |
Section | Mathematics |
Pagination | 3-9 |
Date Published | 7/2017 |
Language | Ukrainian |
Abstract | Substitutions that reduce the equation $u_{tt} = a(t)uu_{xx} + b(t)u_{x}^{2} + c(t)u$ to a system of ordinary differential equations are considered. An efficient method to integrate the corresponding reduced systems is proposed. It is shown that their integration can be reduced to the integration of a system of linear equations $w_{1}^{''} = \Phi_{1}(t)w_{1}$, $w_{2}^{''} = \Phi_{2}(t)w_{2}$, where $\Phi_{1}(t)$ and $\Phi_{2}(t)$ are arbitrary predefined functions.
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Keywords | differential equations, generalized separation of variables, nonlinear hyperbolic equations |
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