368 citations · 615 across the 26 of their papers we have counts for
26 papers
Simple two-layer dispersive models in the Hamiltonian reduction formalism
R. Camassa, G. Falqui, G. Ortenzi +2
A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in two-dimensional doma…
Rogue wave formation scenarios for the focusing nonlinear Schrödinger equation with parabolic-profile initial data on a compact support
F. Demontis, G. Ortenzi, G. Roberti +1
We study the (1+1) focussing nonlinear Schrödinger equation for an initial condition with compactly-supported parabolic profile and phase depending quadratically on the spatial coo…
On blowups of vorticity for the homogeneous Euler equation
B. G. Konopelchenko, G. Ortenzi
Blowups of vorticity for the three- and two- dimensional homogeneous Euler equations are studied. Two regimes of approaching a blowup points, respectively, with variable or fixed t…
On the fine structure and hierarchy of gradient catastrophes for multidimensional homogeneous Euler equation
B. G. Konopelchenko, G. Ortenzi
Blow-ups of derivatives and gradient catastrophes for the -dimensional homogeneous Euler equation are discussed. It is shown that, in the case of generic initial data, the blow-…
Solutions and Singularities of the Semigeostrophic Equations via the Geometry of Lagrangian Submanifolds
Roberto D'Onofrio, Giovanni Ortenzi, Ian Roulstone +1
Using Monge-Ampère geometry, we study the singular structure of a class of nonlinear Monge-Ampère equations in three dimensions, arising in geophysical fluid dynamics. We extend se…
Evolution of interface singularities in shallow water equations with variable bottom topography
R. Camassa, R. D'Onofrio, G. Falqui +2
Wave front propagation with non-trivial bottom topography is studied within the formalism of hyperbolic long wave models. Evolution of non-smooth initial data is examined, and in p…