Exact Analytic Solutions of the Nonlinear Long-Wave Equations in the Case of Axisymmetric Fluid Vibrations in a Parabolic Rotating Vessel |
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Authors: | S F Dotsenko A Rubino |
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Institution: | (1) Okada Pediatrics Clinic, 6-19-12 Okusawa, Setagaya, Tokyo 158-0083, Japan;(2) Research Institute of Electronics, Shizuoka University, 3-5-1 Johoku, Hamamatsu, Shizuoka 432-8011, Japan |
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Abstract: | A class of exact analytic solutions of the system of nonlinear long-wave equations is found. This class corresponds to the axisymmetric vibrations of an ideal incompressible homogeneous fluid in a rotating vessel in the shape of a paraboloid of revolution. The radial velocity of these motions is a linear function, and the azimuthal velocity and free surface displacements are polynomials in the radial coordinate with time-dependent coefficients. The nonlinear vibration frequency is equal to the frequency of the lowest mode of linear axisymmetric standing waves in the parabolic vessel. |
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Keywords: | surface waves nonlinear waves shallow water equation parabolic vessel exact analytic solutions |
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