Том 69
№ 9

Всі номери

Ребенко И. В.

Публікацій: 1
Стаття (українською)

Separation of variables in the two-dimensional wave equation with potential

Жданов Р. З., Ребенко И. В., Фущич В. І.

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Укр. мат. журн. - 1994. - 46, № 10. - С. 1343–1361

The paper is devoted to solution of a problem of separation of variables in the wave equation $u_{tt} - u_{xx} + V(x)u = 0$. We give a complete classification of potentials $V(x)$ for which this equation admits a nontrivial separation of variables. Furthermore, we obtain all coordinate systems that provide separability of the equation considered.