During its periodic motion, a particle floating at the free surface of a water wave experiences
a net drift velocity in the direction of wave propagation, known as the Stokes drift (Stokes …

This book is the written and somewhat expanded version of the author's lectures delivered at
the NSF-CBMS international research conference organized at the Mathematics Department …

We prove that the profile of a periodic traveling wave propagating at the surface of water
above a flat bed in a flow with a real analytic vorticity must be real analytic, provided the …

The interest in the Camassa–Holm equation inspired the search for various generalizations
of this equation with interesting properties and applications. In this Letter we deal with such …

This paper reviews some recent mathematical research activity in the field of nonlinear
geophysical water waves. In particular, we survey a number of exact Gerstner-like solutions …

Analyzing a free boundary problem for harmonic functions in an infinite planar domain, we
prove that in a solitary water wave each particle is transported in the wave direction but …

We present an exact solution of the nonlinear governing equations for geophysical water
waves in the β‐plane approximation near the Equator. The solution describes in the …

We investigate the pressure within an irrotational fluid in a periodic, steady, two‐dimensional
gravity wave above a flat bed. We prove that the pressure in the fluid strictly decreases …

We construct families of two-dimensional travelling water waves propagating under the
influence of gravity in a flow of constant vorticity over a flat bed, in particular establishing the …

In the present study several integrable equations with cubic nonlinearity are derived as
asymptotic models from the classical shallow water theory. The starting point in our …