Small-amplitude, traveling, space periodic solutions–called Stokes waves–of the 2
dimensional gravity water waves equations in deep water are linearly unstable with respect …

A Stokes wave is a traveling free-surface periodic water wave that is constant in the direction
transverse to the direction of propagation. In 1981 McLean discovered via numerical …

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 …

The paper fully answers a long standing open question concerning the stability/instability of
pure gravity periodic traveling water waves—called Stokes waves—at the critical Whitham …

We investigate the spectral instability of a 2 π/κ periodic Stokes wave of sufficiently small
amplitude, traveling in water of unit depth, under gravity. Numerical evidence suggests …

The description of weakly nonlinear water-wave evolution over a horizontal bottom by the
integro-differential Zakharov equation, because of utilising the underlying Hamiltonian …

We develop a numerical method to study eigenvalue problems for operators fundamental to
Stokes wave and its stability in a 2D ideal fluid with a free surface and infinite depth. The …

A stability of nearly limiting Stokes waves to superharmonic perturbations is considered
numerically in approximation of an infinite depth. Investigation of the stability properties can …

We develop a time-dependent conformal method to study the effect of viscosity on steep
surface waves. When the effect of surface tension is included, numerical solutions are found …

We study the stability of Stokes waves in an ideal fluid of infinite depth. The perturbations
that are either coperiodic with a Stokes wave (superharmonics) or integer multiples of its …