This survey covers the mathematical theory of steady water waves with an emphasis on
topics that are at the forefront of current research. These areas include: variational …

The existence of a local curve of corotating and counter-rotating vortex pairs was proven by
Hmidi and Mateu (in Commun Math Phys 350 (2): 699–747, 2017) via a desingularization of …

The Whitham equation is a nonlocal shallow water-wave model which combines the
quadratic nonlinearity of the KdV equation with the linear dispersion of the full water wave …

This paper is concerned with the construction of a new exact solution to the geophysical fluid
dynamics governing equations for inviscid and incompressible fluid in the equatorial region …

We use spherical coordinates to devise a new exact solution to the governing equations of
geophysical fluid dynamics for an inviscid and incompressible fluid with a general density …

We consider nonlinear traveling waves in a two-dimensional fluid subject to the effects of
vorticity, stratification, and in-plane Coriolis forces. We first observe that the terms …

We consider Euler's equations for free surface waves traveling on a body of density stratified
water in the scenario when gravity and surface tension act as restoring forces. The flow is …

We consider the angle θ θ of inclination (with respect to the horizontal) of the profile of a
steady two dimensional inviscid symmetric periodic or solitary water wave subject to gravity …

We prove the nonexistence of two-dimensional solitary gravity water waves with subcritical
wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem …

We present two results on global continuation of monotone front-type solutions to elliptic
PDEs posed on infinite cylinders. This is done under quite general assumptions, and in …