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Solitary waves and fundamental solution for Ostrovsky equation. (English) Zbl 1073.76011
Summary: The Ostrovsky [L. A. Ostrovsky, Okeanologia 12, No. 2, 181–191 (1978)] equation describes the propagation of one-dimensional long waves in shallow water in the presence of rotation (Coriolis effect). In this model dispersion is taken into account and dissipation is neglected. It is proved that existence and non-existence of solitary waves depends on the sign of the dispersion parameter which can be either positive or negative. A fundamental solution of the linear Cauchy problem for Ostrovsky equation is constructed. Special function representation for it is obtained. Some properties of the fundamental solution are established, and its higher-order asymptotics is obtained as the rotation parameter tends to zero.

MSC:
76B25 Solitary waves for incompressible inviscid fluids
76U05 General theory of rotating fluids
35Q51 Soliton equations
86A05 Hydrology, hydrography, oceanography
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