# American Institute of Mathematical Sciences

August  2014, 34(8): 3045-3060. doi: 10.3934/dcds.2014.34.3045

## Small-amplitude equatorial water waves with constant vorticity: Dispersion relations and particle trajectories

 1 Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Wien, Austria, Austria

Received  July 2013 Revised  September 2013 Published  January 2014

We consider the two-dimensional equatorial water-wave problem with constant vorticity in the $f$-plane approximation. Within the framework of small-amplitude waves, we derive the dispersion relations and we find the analytic solutions of the nonlinear differential equation system describing the particle paths below such waves. We show that the solutions obtained are not closed curves. Some remarks on the stagnation points are also provided.
Citation: Delia Ionescu-Kruse, Anca-Voichita Matioc. Small-amplitude equatorial water waves with constant vorticity: Dispersion relations and particle trajectories. Discrete & Continuous Dynamical Systems - A, 2014, 34 (8) : 3045-3060. doi: 10.3934/dcds.2014.34.3045
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##### References:
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