We consider the Whitham equation u t+ 2 uu x+ L ux= 0, where L is the nonlocal Fourier
multiplier operator given by the symbol m (ξ)= tanh⁡ ξ/ξ. GB Whitham conjectured that for …

We investigate the Benjamin–Feir (or modulational) instability of Stokes waves, ie small-
amplitude, one-dimensional periodic gravity waves of permanent form and constant velocity …

Euler's equations govern the behaviour of gravity waves on the surface of an
incompressible, inviscid and irrotational fluid of arbitrary depth. We investigate the spectral …

Abstract Hammack & Segur (1978) conducted a series of surface water-wave experiments in
which the evolution of long waves of depression was measured and studied. This present …

We investigate surface gravity waves in a shallow water tank, in the limit of long
wavelengths. We report the observation of non-stationary dispersive shock waves rapidly …

We propose a shallow water model that combines the dispersion relation of water waves
and Boussinesq equations, and that extends the Whitham equation to permit bidirectional …

We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of the
Kawahara equation. These solutions exhibit high-frequency instabilities when subject to …

We consider the existence of periodic traveling waves in a bidirectional Whitham equation,
combining the full two-way dispersion relation from the incompressible Euler equations with …

We study the existence of traveling wave solutions to a unidirectional shallow water model,
which incorporates the full linear dispersion relation for both gravitational and capillary …

The cubic vortical Whitham equation is a model for wave motion on a vertically sheared
current of constant vorticity in a shallow inviscid fluid. It generalizes the classical Whitham …