▪ Abstract We survey the newly developed Hilbert spectral analysis method and its
applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the …

Oceanic rogue waves are surface gravity waves whose wave heights are much larger than
expected for the sea state. The common operational definition requires them to be at least …

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

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 develop a robust numerical method for modelling nonlinear gravity waves which is
based on the Zakharov equation/mode-coupling idea but is generalized to include …

Freak waves are very large, rare events in a random ocean wave train. Here we study their
generation in a random sea state characterized by the Joint North Sea Wave Project …

A new method valid for highly dispersive and highly nonlinear water waves is presented. It
combines a time-stepping of the exact surface boundary conditions with an approximate …

We have discussed the perturbed Gerdjikov-Ivanov (pGI) equation describing optical pulse
propagation (PP) with perturbation effects, which has various applications in optical fibers …

The modified nonlinear Schrödinger equation of Dysthe [Proc. Roy. Soc. Lond. Ser. A, 369,
105–114 (1979)] is extended by relaxing the narrow bandwidth constraint to make it more …

The nonlinear evolution of deep-water wave groups, which are initiated by unstable three-
wave systems, have been observed in a large wave tank (50 m long, 4.2 m wide, 2.1 m …