Spyridon Kamvissis

Professor of Integrable Systems in Mathematical Physics Department of Applied Mathematics, University of Crete 71409 Knossos-Heraklion, Crete, Greece Office: Γ-103&beta, Main Building Tel: +30 2810 393714 Fax: +30 2810 393701 E-mail: spyros at tem.uoc.gr

Degrees

Ph.D., Courant Institute, 1991

Habilitation, University of Paris VII (Jussieu), 1996

Research

My research focuses on "completely integrable" infinite dimensional Hamiltonian systems, like the KdV equation, the nonlinear Schrödinger equation or the Toda lattice. I am particularly interested in asymptotic problems like the investigation of the long time asymptotics or semiclassical and zero dispersion limits (or continuum limits) of solutions of initial and initial-boundary value problems for nonlinear dispersive partial differential equations and nonlinear lattices. My methods include the analysis of Riemann-Hilbert factorization problems on the complex plane or a hyperelliptic Riemann surface and variational problems for logarithmic potentials with external fields. In a sense I am working on a "nonlinear microlocal analysis" that generalises the classical theory of stationary phase and steepest descent. For a detailed exposition of this point of view see this review article.

European Network in Geometry, Mathematical Physics and Applications (Marie Curie RTN)

Methods of Integrable Systems, Geometry, Applied Mathematics (European Science Foundation Scientific Programme)

Selected Publications

Percy Deift, Spyridon Kamvissis, Thomas Kriecherbauer, Xin Zhou, The Toda Rarefaction Problem, Communications in Pure and Applied Mathematics, v.49, n.1, pp. 35--83, 1996.

Spyridon Kamvissis, Long Time Behavior for the Focusing Nonlinear Schroedinger Equation with Real Spectral Singularities, Communications in Mathematical Physics, v.180, n.2, pp.325-341, 1996.

Spyridon Kamvissis, Semiclassical Nonlinear Schrödinger on the Half Line, Journal of Mathematical Physics, v.44, n.12, 2003.

Spyridon Kamvissis, Kenneth D. T.-R. McLaughlin, Peter D. Miller, Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation, Annals of Mathematics Study 154, Princeton University Press, Princeton, NJ, 2003.

S. Kamvissis, E. A. Rakhmanov, Existence and Regularity for an Energy Maximization Problem in Two Dimensions, Journal of Mathematical Physics, v.46, n.8, 2005;
comment/addendum: revision of the last appendix, Journal of Mathematical Physics, v.50, n.10, 2009.

Spyridon Kamvissis, Gerald Teschl, Stability of the Periodic Toda Lattice under Short Range Perturbations, arXiv:0705.0346, submitted.

More Publications

in MathSciNet

in arXiv

Teaching

XEIMEPINO 2009: ANAΛYΣH I (TEM-141).

YΛH: KEΦ. 1 - 5 (EKTO&Sigma 1.5, 2.7, 5.5) AΠO ΣHMEIΩΣEI&Sigma

EAPINO 2010: MΔE II (METAΠTYXIAKO).

YΛH: Lawrence C. Evans, Partial Differential Equations, AMS, KEΦ. 5,6,7.1

Non-linear dispersive waves

A general approach to linear and non-linear dispersive waves using a Lagrangian

Two-timing, variational principles and waves

Small Dispersion Limit of KdV, Part I

Small Dispersion Limit of KdV, Part II

Small Dispersion Limit of KdV, Part III

Existence and Modulation of Traveling Waves in Particle Chains

XEIMEPINO 2010: ΣTOXAΣTIKEΣ ANEΛIΞEIΣ I (TEM-261).

YΛH: AΠO ΣHMEIΩΣEI&Sigma

EAPINO 2011: APMONIKH ANAΛYΣH (B4-METAΠTYXIAKO).

ΩPEΣ ΓPAΦEIOY: TPITH 3-5, TETAPTH 1-3