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Existence of periodic traveling wave solutions for the Ostrovsky equation. (English) Zbl 1156.35459

Summary: We are concerned with the Ostrovsky equation, which is derived from the theory of weakly nonlinear long surface and internal waves in shallow water under the presence of rotation. On the basis of the variational method, we show the existence of periodic traveling wave solutions.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q35 PDEs in connection with fluid mechanics
35B10 Periodic solutions to PDEs
49J40 Variational inequalities
35A15 Variational methods applied to PDEs
76U05 General theory of rotating fluids
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References:

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