| Subject: | Differential Equations |
| Degree: | Department of Mathematics, National and Kapodistrian University of Athens |
| PhD: | Department of Mathematics, National and Kapodistrian University of Athens, PhD Thesis: Asymptotic Behavior of Semilinear Wave Equations on R^n |
| Research Interests: | Infinite Dimensional Dynamical Systems, Partial Differential Equations |
| Office: | 222, 2nd Floor, Building A |
| Contact with students: | Wednesday 17:00-18:00 & Thursday 14:00-15:00 |
| Tel: | +3022310 60170 |
| E-mail: | karan@uth.gr |
| Personal Webpage: | http://karan.users.uth.gr/ |
Nikos Karachalios received his B. Sc. in Mathematics («Ptychion») from National and Kapodistrian University of Athens in 1994, his M. Sc. with distinction in the Mathematics of Nonlinear Models from the University of Edinburgh in 1995 and his Ph. D. in Partial Differential Equations from the National Technical University of Athens («Ethniko Metsovio Polytecneio» , ΕΜΠ) 1999. After a long-time service in the Department of Mathematics of the University of the Aegean, he currently serves in the Department of Mathematics of the University of Thessaly as a Professor. He has also a long-time experience in long-distance education at a postgraduate level as an adjunct faculty member of Hellenic Open University (EAΠ).
His research interests revolve around the analysis and dynamics of nonlinear partial differential equations and nonlinear lattices. Latest research is focused in the existence and stability properties of localized structures and nonlinear waves in continuous and discrete media.
He has supervised 2 Ph. D. theses and more than 60 postgraduate dissertations.
Further details for his curriculum vitae, research output and activities in the Department are given in his personal web-page: http://karan.users.uth.gr/
- D. Hennig and N. I. Karachalios. Dynamics of nonlocal and local discrete Ginzburg-Landau equations: global attractors and their congruence. Nonlinear Analysis 215 (2022), Paper No. 112647.
- S. Diamantidis, T. P. Horikis and N. I. Karachalios. Exciting extreme events in the damped and AC-driven NLS equation through plane wave initial conditions Chaos 31 (2021), no. 5, 053103, (20 pp).
- N. Gialelis, N. I. Karachalios and I. G. Stratis. Regularity of nonvanishing-at infinity or at the boundary-solutions of the defocusing nonlinear Schrödinger equation. Communications in Partial Differential Equations 46 (2021) 233-281 (49pp).
- N. I. Karachalios, P. Kyriazopoulos and K. Vetas. The Lefever-Lejeune nonlinear lattice: convergence dynamics and the structure of equilibrium states. Physica D: Nonlinear Phenomena 409 (2020), 132487 (21pp).
- V. Achilleos, S. Diamantidis, D. J. Frantzeskakis, N. I. Karachalios and P. G. Kevrekidis. Conservation laws, exact travelling waves and modulation instability for an extended nonlinear Schrödinger equation. Journal of Physics A: Mathematical and Theoretical 48 (2015) no. 35, 355205 (33 pp).
- N. I. Karachalios, Bernardo Sánchez-Rey, P.G. Kevrekidis and J. Cuevas. Breathers for the Discrete Nonlinear Schrödinger equation with nonlinear hopping. Journal of Nonlinear Science 23 (2013), no. 2, 205-239.
- J. Cuevas, J. C. Eilbeck and N. I. Karachalios. Thresholds for breather solutions of the Discrete Nonlinear Schrödinger equation with saturable and power nonlinearity. Discrete and Continuous Dynamical Systems-Series A 21 (2008) no.2, 445-475.
- N. I. Karachalios and N. Zographopoulos. On the dynamics of a degenerate parabolic equation: Global bifurcation of stationary states and convergence. Calculus of Variations and Partial Differential Equations 25 (2006), no. 3, 361-393.
- N. I. Karachalios and A. N. Yannacopoulos. Global existence and global attractors for the Discrete Nonlinear Schrödinger equation. Journal of Differential Equations 217 (2005) no. 1, 88-123.
