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On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons. (English) Zbl 1088.35531
Summary: Detailed analysis of solitary and periodic stationary solutions of the reduced Ostrovsky equation is presented. The full Ostrovsky equation \[ (u_{t} + c_{0}u_{x} + \alpha uu_{x} + \beta u_{xxx})_{x} = \gamma u \] was derived in 1978 for oceanic waves affected by Earth rotation, and its reduced form without small-scale dispersion, \[ (u_{t} + c_{0}u_{x} + \alpha uu_{x})_{x} = \gamma u, \] was pointed out in his original paper and then, derived later by many authors in different physical contexts. However, some aspects of stationary solutions to the last equation remained unclear so far. An attempt to introduce clarity to this problem is undertaken in this paper.

35Q35 PDEs in connection with fluid mechanics
86A05 Hydrology, hydrography, oceanography
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Full Text: DOI
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