Exact solutions of the nonliear equation $u_{tt} = = a(t) uu_{xx} + b(t) u_x^2 + c(t) u $
Ans¨atzes that reduce the equation$u_{tt} = = a(t) uu_{xx} + b(t) u_x^2 + c(t) u $ to a system of two ordinary differential equations are defined. Also it is shown that the problem of constructing exact solutions of the form $u = \mu 1(t)x_2 + \mu 2(t)x\alpha , \alpha \in \bfR$, to this equation,...
Збережено в:
| Дата: | 2017 |
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| Автори: | , , , , , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2017
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1768 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | Ans¨atzes that reduce the equation$u_{tt} =
= a(t) uu_{xx} + b(t) u_x^2 + c(t) u $ to a system of two ordinary differential equations are defined. Also it is shown that the problem of constructing exact solutions of the form $u = \mu 1(t)x_2 + \mu 2(t)x\alpha , \alpha \in \bfR$,
to this equation, reduces to integrating of a system of linear equations $\mu \prime \prime
1 = \Phi 1(t)\mu 1, \mu \prime \prime
2 = \Phi 2(t)\mu 2$, where $\Phi 1(t)$ and
\Phi 2(t) are arbitrary predefined functions. |
|---|