On three-dimensional Gerstner-like equatorial water waves.

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 which have been derived to model various geophysical oceanic waves, and wave-current interactions, in the equatorial region. These solutions are nonlinear, three-dimensional and explicit in terms of Lagrangian variables.This article is part of the theme issue 'Nonlinear water waves'.