5 papers
Learning Lax Pairs: Revisiting the Classical Paradigm
Jimmie Adriazola, Gino Biondini, Wei Zhu +1
A Lax pair is sometimes thought of as a structural certificate, in that the spatial operator carries the spectral data of an integrable system, and its isospectral evol…
Kinetic equations for a two-dimensional soliton gas
Gino Biondini, Thibault Bonnemain, Benjamin Doyon +2
We formulate a general system of kinetic equations for a non-stationary two-dimensional gas of elastically interacting line solitons and apply it to the description of a soliton ga…
Spectral theory for self-adjoint Dirac operators with periodic potentials and inverse scattering transform for the defocusing nonlinear Schroedinger equation with periodic boundary conditions
Gino Biondini, Zechuan Zhang
The inverse spectral theory for a self-adjoint one-dimensional Dirac operator associated periodic potentials is formulated via a Riemann-Hilbert problem approach. The resulting for…
Semiclassical dynamics and coherent soliton ensembles in the derivative nonlinear Schrödinger equation with periodic initial conditions
Zachery Wolski, Zechuan Zhang, Gino Biondini +1
The semiclassical limit of the derivative nonlinear Schrodinger equation with periodic initial conditions is studied analytically and numerically. The spectrum of the associated sc…
Spectral theory for non-self-adjoint Dirac operators with periodic potentials and inverse scattering transform for the focusing nonlinear Schrödinger equation with periodic boundary conditions
Gino Biondini, Gregor KovaÄiÄ, Alexander Tovbis +2
We formulate the inverse spectral theory for a non-self-adjoint one-dimensional Dirac operator associated periodic potentials via a Riemann-Hilbert problem approach. We use the res…