In this essay we give an overview on the problem of rogue or freak wave formation in the
ocean. The matter of the phenomenon is a sporadic occurrence of unexpectedly high waves …

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 …

In spite of the huge progress in studies on solitary waves in the seventies and eighties of the
XX century as well as their practical importance, the theory of solitons is far from being …

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 …

In optical fibres, weak modulations can grow at the expense of a strong pump to form a
triangular comb of sideband pairs, until the process is reversed. Repeated cycles of such …

Numerical simulation of evolution of nonlinear gravity waves is presented. Simulation is
done using two-dimensional code, based on conformal mapping of the fluid to the lower half …

Formation of waves of large amplitude (freak waves, killer waves) at the surface of the ocean
is studied numerically. We have observed that freak waves have the same ratio of the wave …

We characterize the long‐time asymptotic behavior of the focusing nonlinear Schrödinger
(NLS) equation on the line with symmetric, nonzero boundary conditions at infinity by using …

We consider the modulational instability of nonlinearly interacting two-dimensional waves in
deep water, which are described by a pair of two-dimensional coupled nonlinear …

This paper is concerned with initial-boundary-value problems (IBVPs) for a class of
nonlinear Schrödinger equations posed either on a half line R+ or on a bounded interval (0 …