94 citations · 404 across the 21 of their papers we have counts for
20 papers
x-periodic Quasi One Dimensional Anomalous (Rogue) Waves in Multidimensional Nonlinear Schrödinger Equations: Fission, Fusion, and Recurrence
Francesco Coppini, Paolo Maria Santini
In a recent work we studied the first nonlinear stage of modulation instability (NLSMI) of x-periodic anomalous (rogue, freak, extreme) waves (AWs) of physically relevant multidime…
Quasi one dimensional anomalous (rogue) waves in multidimensional nonlinear Schrödinger equations 1: fission and fusion
Francesco Coppini, Paolo Maria Santini
In this paper we study the first nonlinear stage of modulation instability (NLSMI) of -periodic AWs in multidimensional generalizations of the focusing nonlinear Schrödinger (NL…
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…
Modulation instability, periodic anomalous wave recurrence, and blow up in the Ablowitz-Ladik lattices
F. Coppini, P. M. Santini
The Ablowitz-Ladik equations, hereafter called and , are distinguished integrable discretizations of respectively the focusing and defocusing nonlinear Schrödinger (NL…
The linear and nonlinear instability of the Akhmediev breather
P. G. Grinevich, P. M. Santini
The Akhmediev breather (AB) and its M-soliton generalization are exact solutions of the focusing NLS equation periodic in space and exponentially localized in time over the…
On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and discontinuous shocks
F. Santucci, P. M. Santini
We study the generalization of the dispersionless Kadomtsev - Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the pro…