Seminar
FOCUSING NONLINEAR SCHRODINGER EQUATION (FNLS), FROM SMALL DISPERSION LIMIT TO SOLITON/BREATHER GASES
by ALEXANDER TOVBIS (UNIVERSITY OF CENTRAL FLORIDA)
Location: 200B.02.18, Leuven
Time: Wednesday September 18, 2019 at
10:30
1D fNLS is an integrable equation which can be integrated by the inverse scattering transform method. The small dispersion (semiclassical) limit of the fNLS is a convenient tool to study large scale space-time behavior of the fNLS evolution of a given initial data (potential). In the process of such evolution, a potential typically develops an increasingly complicated behavior that can be approximated by some special quasi-periodic solutions of the fNLS known as finite-gap or nonlinear multi phase solutions. As number of phases typically grow with time, approximation of a particular solution becomes meaningless at some point, when it makes more sense to look for some ``in large” characteristics of the solutions, such as , for example, the probability density function, the kinetic and potential energy, etc. At this point it also makes sense to talk about gas dynamics of some fNLS related gases, where elementary fNLS solutions such as solitons, breathers, etc. play the role of gas particles. From this point of view, the theory soliton, breather and more general gases can be described in terms of the special high genus limits of hyperelliptic Riemann surfaces, which parametrize the finite gap solutions. I will talk about my recent work in that direction.
