SPYRIDON KAMVISSIS

SPYRIDON KAMVISSIS

My research has focused mostly on "completely integrable" infinite dimensional Hamiltonian systems, like the KdV equation, the nonlinear Schrödinger equation and the Toda lattice. I have been particularly interested in asymptotic problems like the investigation of long time asymptotics, semiclassical 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, including difficult problems involving instabilities (like the so-called modulational instability). 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 theory of variational problems for Green potentials with harmonic external fields. In a sense I have worked on a "nonlinear microlocal analysis" that generalises the classical theory of stationary phase and steepest descent.
SPYRIDON
KAMVISSIS
...
Mathematics Building, University of Crete, Voutes Campus, 70013 Greece
+30 2810 393714
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

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.

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.

Fujiié, S., Kamvissis, S. Semiclassical WKB problem for the non-self-Adjoint Dirac operator with analytic potential, Journal of Mathematical Physics (2020) 61 (1), art. no. 011510.

Hatzizisis, N., Kamvissis, S. Semiclassical WKB problem for the non-self-adjoint Dirac operator with a decaying potential, Journal of Mathematical Physics (2021) 62 (3), art. no. 033510.

Chatziafratis, A., Kamvissis, S., Stratis, I.G. Boundary behavior of the solution to the linear Korteweg-De Vries equation on the half line, Studies in Applied Mathematics (2023) 150 (2), pp. 339-379.
Completely integrable infinite dimensional Hamiltonian systems.
Riemann-Hilbert problems on hyperelliptic curves.
Potential theory and variational problems of electrostatic type in the plane.
PDE theory and initial-boundary value problems for soliton equations.
Asymptotic analysis and nonlinear steepest descent.
Semiclassical asymptotics.
WKB theory.
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