In an annular resonator parametrically driven in the vertical direction, the irrotational movement of an incompressible fluid has been studied by the multiple-scales approach. The calculations have shown that under the condition that the radius of the annular resonator is much larger than the width the displacement of the movement of fluid surface satisfies the cubic Schrodinger equation. A non-propagating surface-wave solitons solution is obtained that describes the standing solitary wave observed by Wu, Keolian and Rudnick (1984).
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