Spyridon Kamvissis

Professor of Integrable Systems in Mathematical Physics, University of Crete
Member, Institute of Applied and Computational Mathematics, Foundation for Research & Technology - Hellas (FORTH)
Office: Δ338, Mathematics Building, 70013 Voutes, Greece
Tel: +30 2810 393714
E-mail: Spyridon "dot" Kamvissis "at" amias "dot" ias "dot" edu

Degrees

Ph.D., Courant Institute, 1991

Habilitation, University of Paris 7, 1996

Research and Selected Publications

My research has focused mostly on infinite dimensional Hamiltonian systems that admit a Lax pair or a zero curvature condition and can be studied via an inverse scattering/spectral method. I have been particularly interested in mathematically rigorous treatments of asymptotic problems like the investigation of long time asymptotics, semiclassical high frequency asymptotics, zero dispersion limits and continuum limits of solutions of initial and initial-boundary value problems for nonlinear dispersive partial differential equations and nonlinear lattices, with particular attention to delicate "universal model" problems displaying intricate instabilities. I have used and extended techniques from PDE theory, complex analysis, harmonic analysis, potential theory and algebraic geometry. Along the way, I have made contributions to the analysis of Riemann-Hilbert factorisation problems on the complex plane or a hyperelliptic Riemann surface and the related theory of variational problems for Green potentials with harmonic external fields. In a sense I have worked on a "nonlinear/non-commutative 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.

Spyridon Kamvissis, On the Long Time Behavior of the Doubly Infinite Toda Lattice under Initial Data Decaying at Infinity, Communications in Mathematical Physics, v.153, n.3, pp.479-519, 1993

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 Schrödinger Equation with Real Spectral Singularities, Communications in Mathematical Physics, v.180, n.2, pp.325-341, 1996 (revised)

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 (revised)

Spyridon Kamvissis, Gerald Teschl, Stability of Periodic Soliton Equations under Short Range Perturbations, Phys. Lett. A 364-6, 480-483 (2007)
Spyridon Kamvissis, A Riemann-Hilbert Problem in a Riemann Surface; invited contribution to a volume honoring P.D.Lax on his 85th birthday, Acta Mathematica Scientia, v.31, n.6, November 2011, pp. 2233-2246.
Spyridon Kamvissis, Gerald Teschl, Long Time Asymptotics of the Periodic Toda Lattice under Short Range Perturbations, Journal of Mathematical Physics, v.53, n.7, 2012

D. C. Antonopoulou, S. Kamvissis, On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the Half-Line, Nonlinearity 28 (2015) 3073-3099 + Addendum (2016)
A.F.Pallas Analysis Prize of the Academy of Athens (2016)

Setsuro Fujiie, Spyridon Kamvissis, Semiclassical WKB problem for the non-self-adjoint Dirac operator with analytic potential, Journal of Mathematical Physics, v.61, n.1, 011510, 2020
Nicholas Hatzizisis, Spyridon Kamvissis, Semiclassical WKB problem for the non-self-adjoint Dirac operator with a decaying potential, Journal of Mathematical Physics, v.62, n.3, 033510, 2021
Nicholas Hatzizisis, Spyridon Kamvissis, Semiclassical WKB Problem for the Non-Self-Adjoint Dirac Operator with a Multi-Humped Decaying Potential, arXiv 2106.07253
Setsuro Fujiie, Nicholas Hatzizisis, Spyridon Kamvissis, Semiclassical WKB Problem for the non-self-adjoint Dirac operator with an analytic rapidly oscillating potential, arXiv 2204.07089