35 citations · 118 across the 6 of their papers we have counts for
6 papers
The effect of a small loss or gain in the periodic NLS anomalous wave dynamics. I
F. Coppini, P. G. Grinevich, P. M. Santini
The focusing Nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media,…
The finite gap method and the periodic NLS Cauchy problem of the anomalous waves, for a finite number of unstable modes
P. G. Grinevich, P. M. Santini
The focusing Nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media,…
Numerical instability of the Akhmediev breather and a finite-gap model of it
P. G. Grinevich, P. M. Santini
In this paper we study the numerical instabilities of the NLS Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting our consid…
The finite gap method and the analytic description of the exact rogue wave recurrence in the periodic NLS Cauchy problem. 1
P. G. Grinevich, P. M. Santini
The focusing NLS equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, considered the main phy…
Newtonian dynamics in the plane corresponding to straight and cyclic motions on the hyperelliptic curve : ergodicity, isochrony, periodicity and fractals
P. G. Grinevich, P. M. Santini
We study the complexification of the one-dimensional Newtonian particle in a monomial potential. We discuss two classes of motions on the associated Riemann surface: the rectilinea…
The initial boundary value problem on the segment for the Nonlinear Schrödinger equation; the algebro-geometric approach. I
P. G. Grinevich, P. M. Santini
This is the first of a series of papers devoted to the study of classical initial-boundary value problems of Dirichlet, Neumann and mixed type for the Nonlinear Schrödinger equatio…