The physics of the one-dimensional nonlinear Schrödinger equation in fiber optics: Rogue waves, modulation instability and self-focusing phenomena
We review the different dynamical mechanisms leading to the emergence of coherent
structures in physical systems described by the integrable one-dimensional nonlinear …
structures in physical systems described by the integrable one-dimensional nonlinear …
Bound state soliton gas dynamics underlying the spontaneous modulational instability
We investigate the fundamental phenomenon of the spontaneous, noise-induced
modulational instability (MI) of a plane wave. The statistical properties of the noise-induced …
modulational instability (MI) of a plane wave. The statistical properties of the noise-induced …
The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes
PG Grinevich, PM Santini - Russian Mathematical Surveys, 2019 - iopscience.iop.org
The focusing non-linear Schrödinger (NLS) equation is the simplest universal model
describing the modulation instability (MI) of quasimonochromatic waves in weakly non-linear …
describing the modulation instability (MI) of quasimonochromatic waves in weakly non-linear …
Nonlinear evolution of the locally induced modulational instability in fiber optics
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 …
instability of a plane wave in the presence of a localized perturbation. Using a recirculating …
The finite gap method and the analytic description of the exact rogue wave recurrence in the periodic NLS Cauchy problem. 1
PG Grinevich, PM Santini - Nonlinearity, 2018 - iopscience.iop.org
The focusing nonlinear Schrödinger (NLS) equation is the simplest universal model
describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear …
describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear …
[HTML][HTML] The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes
PG Grinevich, PM Santini - Physics Letters A, 2018 - Elsevier
Abstract The focusing Nonlinear Schrödinger (NLS) equation is the simplest universal model
describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear …
describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear …
Nonlinear localization of dissipative modulation instability
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 …
complete disintegration of a plane wave background. Here we report on experiments …
Formation of rogue waves from a locally perturbed condensate
AA Gelash - Physical Review E, 2018 - APS
The one-dimensional focusing nonlinear Schrödinger equation (NLSE) on an unstable
condensate background is the fundamental physical model that can be applied to study the …
condensate background is the fundamental physical model that can be applied to study the …
Universal behavior of modulationally unstable media
Evidence is presented of universal behavior in modulationally unstable media. An ensemble
of nonlinear evolution equations, including three partial differential equations, an integro …
of nonlinear evolution equations, including three partial differential equations, an integro …
From modulational instability to focusing dam breaks in water waves
We report water wave experiments performed in a long tank where we consider the
evolution of nonlinear deep-water surface gravity waves with the envelope in the form of a …
evolution of nonlinear deep-water surface gravity waves with the envelope in the form of a …