E. Bettelheim
Title: Nonlinear Dynamics of Quantum Systems and Soliton
Theory
Abstract: we show that space-time evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify the space-time dependence of matrix elements of fermions appearing in certain physical applications with the tau function of the modified KP-hierarchy. The established relation allows us to apply the apparatus of soliton theory to the study of non-linear aspects of quantum dynamics. We also describe bosonization in momentum space - a representation of a fermion operator by a Bose field in the presence of a boundary state. The work was done in collaboration with A. G. Abanov and P. Wiegmann.
T. Claeys ( .pdf of the talk )
Title: Critical asymptotics for the Korteweg-de Vries equation in
the
small
dispersion limit
E. Ferapontov
Title: On the integrability of symplectic Monge-Ampere
equations
Joint work with B Doubrov
D. Guzzetti ( .pdf of the talk )
Title: On the asymptotic behavior of PVI functions: a matching method
C. Klein ( .pdf of the talk )
Title: Semiclassical limit of the focusing NLS equation
We study the semiclassical limit of the focusing NLS equation near the point of gradient catastrophe of the corresponding dispersionless equations. It is argued that the NLS slution near this points is asymptotically given by the tritronquèe solution of the Painlevè I equation. We present numerical evidence for this conjecture. We compare NLS in this limit with the dispersionless limit for KdV.
K. McLaughlin ( .pdf of the talk )
Title:Universality in Random Matrix Theory: F(Tr(V(M)) instead of Tr(V(M))
Abstract: We'll start with the usual random Hermitian matrices as an introduction. Then we'll consider an example of a probability measure on random Hermitian matrices which are invariant ensembles but which have peculiar, and different behavior. The primary goal will be to summarize explicit formulae for eigenvalue statistics, and with remaining time, discuss the subsequent asymptotic analysis.
P. Miller (.pdf of the
talk and three movie files that are linked to therein )
Title: The
zero-dispersion limit of the Benjamin-Ono equation
A. Moro
Title: Soliton equations in 2 + 1 dimensions: deformations of
dispersionless limits
Abstract:
We demonstrate that hydrodynamic reductions of
dispersionless integrable systems in
2+1 dimensions, such as the dispersionless
Kadomtsev-Petviashvili (dKP) and dispersionless
Toda lattice (dTl) equations, can be deformed into
reductions of the corresponding dispersive
counterparts. Conversely, the requirement that any
hydrodynamic reduction possesses a
deformation of this kind imposes strong constraints on
dispersive terms and proves to be an
efficient classification criterion for integrable systems in
2 + 1-dimensions.
In particular, we classify scalar third order soliton
equations in 2 + 1 dimensions which
generalize the examples of KP, Veselov-Novikov and Harry
Dym equations. Our procedure leads to a list of integrable
third order equations, some of which are apparently new.
M. Onorato ( .pdf of the talk )
Title: Numerical simulation of ocean
waves
V. Sciacca ( .pdf of the talk )
Title: Complex singularities tracking methods for Pdes
A. Shagalov ( .pdf of the talk )
Control of nonlinear
periodic
waves, numerical
aspects
Abstract: the technique to control dynamics of multi-phase waves in NLS and SG equations by a small resonant driving is proposed. The approach is based on the idea of "autoresonance". The numerics essentially use the direct spectral transform to describe excitation and control of finite-gap solutions