Auto-modulation versus breathers in the nonlinear stage of modulational instability.

The nonlinear stage of modulational instability in optical fibers induced by a wide and easily accessible class of localized perturbations is studied using the nonlinear Schrödinger equation. It is shown that the development of associated spatio-temporal patterns is strongly affected by the shape and the parameters of the perturbation. Different scenarios are presented that involve an auto-modulation developing in a characteristic wedge, possibly coexisting with breathers which lie inside or outside the wedge.

Solitons and rogue waves in spinor Bose-Einstein condensates.

We present a general classification of one-soliton solutions as well as families of rogue-wave solutions for F=1 spinor Bose-Einstein condensates (BECs). These solutions are obtained from the inverse scattering transform for a focusing matrix nonlinear Schrödinger equation which models condensates in the case of attractive mean-field interactions and ferromagnetic spin-exchange interactions. In particular, we show that when no background is present, all one-soliton solutions are reducible via unitary transformations to a combination of oppositely polarized solitonic solutions of single-component BECs.

Recurrence due to periodic multisoliton fission in the defocusing nonlinear Schrödinger equation.

We address the degree of universality of the Fermi-Pasta-Ulam recurrence induced by multisoliton fission from a harmonic excitation by analyzing the case of the semiclassical defocusing nonlinear Schrödinger equation, which models nonlinear wave propagation in a variety of physical settings. Using a suitable Wentzel-Kramers-Brillouin approach to the solution of the associated scattering problem we accurately predict, in a fully analytical way, the number and the features (amplitude and velocity) of solitonlike excitations emerging post-breaking, as a function of the dispersion smallness parameter. This also permits us to predict and analyze the near-recurrences, thereby inferring the universal character of the mechanism originally discovered for the Korteweg-deVries equation.

Oscillation structure of localized perturbations in modulationally unstable media.

We characterize the properties of the asymptotic stage of modulational instability arising from localized perturbations of a constant background, including the number and location of the individual peaks in the oscillation region. We show that, for long times, the solution tends to an ensemble of classical (i.e.