5 papers
On perturbations of the spectrum of one-dimensional PT-symmetric periodic Schrodinger operator
P. G. Grinevich, I. A. Taimanov
For PT-symmetric periodic Schrodinger operator, which is a small perturbation of the zero potential, we calculate the spectrum and the divisor of zeroes of the Bloch function in th…
The periodic N breather anomalous wave solution of the Davey-Stewartson equations; first appearance, recurrence, and blow up properties
F. Coppini, P. G. Grinevich, P. M. Santini
The integrable focusing Davey-Stewarson (DS) equations, multidimensional generalizations of the focusing cubic nonlinear Schrödinger (NLS) equation, provide ideal mathematical mode…
The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 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,…
An integral geometry lemma and its applications: the nonlocality of the Pavlov equation and a tomographic problem with opaque parabolic objects
P. G. Grinevich, P. M. Santini
As in the case of soliton PDEs in 2+1 dimensions, the evolutionary form of integrable dispersionless multidimensional PDEs is non-local, and the proper choice of integration consta…
Nonlocality and the inverse scattering transform for the Pavlov equation
P. G. Grinevich, P. M. Santini
As in the case of soliton PDEs in 2+1 dimensions, the evolutionary form of integrable dispersionless multidimensional PDEs is non-local, and the proper choice of integration consta…