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Small-amplitude steady water waves on flows with counter-currents.

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NWWW01 - Nonlinear water waves

The two-dimensional free-boundary problem describing steady  gravity waves with vorticity is considered for water of finite depth. It is known that the whole set of small-amplitude waves on unidirectional rotational flows is exhausted by Stokes and solitary waves. In the case of flows with counter-currents, there occur other patterns of behaviour. Two results of this kind will be discussed. The first one concerns the existence of N-modal steady waves, whereas the second result deals with the following fact.    If the number of roots of the dispersion equation is greater than one, then the major part of the plethora of small-amplitude waves is represented by non-symmetric ones. This is a joint work with E. Lokharu, Lund University.

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