We review the different dynamical mechanisms leading to the emergence of coherent
structures in physical systems described by the integrable one-dimensional nonlinear …

The double-periodic solutions of the focusing nonlinear Schrödinger equation have been
previously obtained by the method of separation of variables. We construct these solutions …

It is shown how to compute the instability rates for the double-periodic solutions to the cubic
NLS (nonlinear Schrödinger) equation by using the Lax linear equations. The wave function …

We report an optical fiber experiment in which we study the nonlinear stage of modulational
instability of a plane wave in the presence of a localized perturbation. Using a recirculating …

Solitons on a finite background, also called breathers, are solutions of the focusing
nonlinear Schrödinger equation, which play a pivotal role in the description of rogue waves …

We present exact solutions for rogue waves arising on the background of periodic standing
waves in the focusing nonlinear Schrödinger equation. The exact solutions are obtained by …

We report an experimental study on the modulation instability process and associated rogue
breathers for the case of stationary periodic background waves, namely dnoidal and cnoidal …

We show that the nonlinear stage of the universal phenomenon of modulational instability,
and in particular its recurrent behavior, is deeply affected by arbitrarily weak losses. Indeed …

A systematic approach for constructing exact periodic-background solutions of integrable
nonlinear evolution equations associated with 3× 3 spectral problems is developed by …

Modulation instability (MI) in the presence of noise typically leads to an irreversible and
complete disintegration of a plane wave background. Here we report on experiments …