Since time immemorial, surface water waves and their subsequent breaking have been
studied. Herein we concentrate on breaking surface waves in deep and intermediate water …

Page 1 Mathematical Surveys and Monographs Volume 188 The Water Waves Problem
Mathematical Analysis and Asymptotics David Lannes American Mathematical Society Page 2 …

The field of nonlinear dispersive waves has developed enormously since the work of Stokes,
Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s …

Page 1 The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse Catherine
Sulem Pierre-Louis Sulem Springer Page 2 Applied Mathematical Sciences Volume 139 Editors …

A review of physical mechanisms of the rogue wave phenomenon is given. The data of
marine observations as well as laboratory experiments are briefly discussed. They …

We prove the existence and the linear stability of Cantor families of small amplitude time
quasi-periodic standing water wave solutions—namely periodic and even in the space …

This paper presents the recent development on the nonlinear directional wave generation
process in a 3D Numerical Wave Tank (NWT). The NWT is based on a nonlinear model …

We consider the gravity water waves system in the case of a one dimensional interface, for
sufficiently smooth and localized initial data, and prove global existence of small solutions …

The instability of Stokes waves, steady propagating waves on the surface of an ideal fluid of
infinite depth, is a fundamental problem in the field of nonlinear science. The dominant …

We are interested in the system of gravity water waves equations without surface tension.
Our purpose is to study the optimal regularity thresholds for the initial conditions. In terms of …