67 citations · 82 across the 4 of their papers we have counts for
5 papers
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…
The Cauchy problem for the Pavlov equation
P. G. Grinevich, P. M. Santini, D. Wu
Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the r…
Holomorphic eigenfunctions of the vector field associated with the dispersionless Kadomtsev-Petviashvili equation
P. G. Grinevich, P. M. Santini
Vector fields naturally arise in many branches of mathematics and physics. Recently it was discovered that Lax pairs for many important multidimensional integrable partial differen…