Panayotis G. Kevrekidis, Professor
Office LGRT 1524
Phone (413) 577-1977
Fax (413) 545-1801
Email kevrekid <at> math.umass.edu
Mailing Address
Department of Mathematics and Statistics
Lederle Graduate Research Tower
University of Massachusetts
Amherst, MA 01003-9305
Education  
Ph.D. Rutgers University, 2000
M.Phil. Rutgers University, 2000
M.S. Rutgers University, 1998
B.Sc. University of Athens, 1996
Research Interests: Mathematical Physics; Nonlinear PDEs and DDEs; Dynamical Systems; Mathematical Biology
Professor Kevrekidis studies a variety of systems chiefly stemming from the mathematical physics of optical systems (waveguide arrays and optical fibers), as well as from the soft-condensed matter setting of Bose-Einstein Condensates. The research mainly revolves around the existence, stability and dynamics of localized (solitary wave) structures in such one-, two- and three-dimensional setups, often described by equations of Nonlinear Schrodinger or Klein-Gordon type. While the settings under study are principally Hamiltonian in nature (often featuring external potentials, or being genuinely discrete and posed on, so-called, dynamical lattices), occasionally dissipative perturbations thereof are also considered. Besides this main thrust of research Professor Kevrekidis also maintains a wide variety of additional interests including mathematical biology [especially tumor angionesis, nephron dynamics and DNA models], simple cosmological models, the nucleation of liquid droplets in the atmosphere, gelation and related phase transition phenomena in polymers, aerosol dynamics in the atmosphere and in the human body [inhalation and desposition of particles in the respiratory tract], catalytic chemistry and reaction-diffusion models, and dynamics and energy landscapes of glassy materials among others.
Current Teaching: Math 532, Fall 2013
Current Teaching: Math 691Y, Fall 2013
Previous Teaching
Math 532, Topics in Ordinary Differential Equations, Fall 12
Math 132, Calculus II, Course Chair and Section F Fall 11
Math 534, Introduction to Partial Differential Equations Spring 11
Math 132, Calculus II, Course Chair and Section F Fall 10
Math 534, Introduction to Partial Differential Equations Spring 10
Math 532, Topics in Ordinary Differential Equations, Fall 09
Math 597-697Y, Nonlinear Dynamical Lattices, Spring 09
Math 132, Calculus II, Course Chair and Section E Fall 08
Math 534, Introduction to Partial Differential Equations, Spring 07
Math 691, Applied Math M.S. Project, Fall 06-Spring 07 (co-taught with N. Whitaker)
Math 534, Introduction to Partial Differential Equations, Spring 06
Math 132, Calculus II, Course Chair and Sections 4-5, Fall 05
Math 652, Graduate Numerical Analysis, Part II, Spring 05
Math 132, Calculus II, Section 2, Fall 04
Math 651, Graduate Numerical Analysis, Part I, Fall 04
Math 127, Calculus for Business and Life Sciences, Section 3, Spring 04
Math 132, Calculus II, Sections 1 and 3, Fall 03
Math 132H, Honors Calculus II, Spring 03
Math 534, Introduction to Partial Differential Equations, Spring 03
Math 132, Fall 02, Course Chair and Section 7
Math 132, Calculus II, Spring 02
Math 131, Calculus I, Fall 01
Some Recent Preprints from www.arXiv.org
Selected Publications
N.J. Balmforth, R.V. Craster and P.G. Kevrekidis, Being Stable and Discrete, Physica 135D, 212-232 (2000)
P.G. Kevrekidis and M.I. Weinstein, Dynamics of Lattice Kinks, Physica 142D, 113-152 (2000)
T. Kapitula and P. Kevrekidis, Stability of Waves in Discrete Systems, Nonlinearity 14, 533-566 (2001).
B.A. Malomed and P.G. Kevrekidis, Discrete Vortex Solitons, Phys. Rev. E 64, 026601, 6 pages (2001).
P.G. Kevrekidis, K.O. Rasmussen and A.R. Bishop, The Discrete Nonlinear Schrodinger Equation: A Survey of Recent Results, Int. J. of Mod. Phys. B 15, 2833-2900 (2001).
A. Smerzi, A. Trombettoni, P.G. Kevrekidis and A.R. Bishop, Superfluid-Insulator Transition in a Chain of Weakly Coupled Bose-Einstein Condensates, Phys. Rev. Lett. 89, 170402, 4 pages (2002)
G.L. Alfimov, P.G. Kevrekidis, V.V. Konotop and M. Salerno, Wannier function analysis of the nonlinear Schrodinger equation with a periodic potential, Phys. Rev. E 66, 046608, 5 pages (2002)
C.I. Siettos, I.G. Kevrekidis and P.G. Kevrekidis, Focusing Revisited: a Renormalization/Bifurcation Approach, Nonlinearity 16, 497-506 (2003).
P.G. Kevrekidis, G. Theocharis, D.J. Frantzeskakis, and Boris A. Malomed, Feshbach Resonance Management for Bose-Einstein Condensates, Phys. Rev. Lett. 90, 230401 (2003).
T.Kapitula, P.G. Kevrekidis and B. Sandstede, Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems, Physica D 195, 263-282 (2004).
A. Stefanov and P.G. Kevrekidis, Asymptotic behavior of small solutions for the discrete nonlinear Schrodinger and Klein-Gordon equations, Nonlinearity 18, 1841-1857 (2005).
D.E. Pelinovsky, P.G. Kevrekidis and D.J. Frantzeskakis, Stability of discrete solitons in Nonlinear Schrodinger Lattices, Physica D 212, 1-19 (2005).
D.E. Pelinovsky, P.G. Kevrekidis and D.J. Frantzeskakis, Persistence and stability of discrete vortices in nonlinear Schrodinger lattices, Physica D 212, 20-53 (2005).
T. Kapitula and P.G. Kevrekidis, Bose-Einstein Condensates in the presence of a magnetic trap and an optical lattice: two-mode approximation, Nonlinearity 18, 2491-2512 (2005).
X. Wang, Z. Chen and P.G. Kevrekidis, Observation of discrete solitons and soliton rotation in optically-induced periodic ring lattices, Phys. Rev. Lett. 96, 083904, 4 pages (2006).
P.G. Kevrekidis and D.E. Pelinovsky, Discrete Vector on-site Vortices, Proceedings of the Royal Society of London A 462, 2671-2694 (2006).
M. Centurion, M.A. Porter, P.G. Kevrekidis and D. Psaltis, Nonlinearity Management in Optics: Experiment, Theory and Simulation, Phys. Rev. Lett. 97, 033903, 4 pages (2006).
T.R.O. Melvin, A.R. Champneys, P.G. Kevrekidis and J. Cuevas, Radiationless Travelling Waves in Saturable Nonlinear Schrodinger Lattices, Phys. Rev. Lett. 97, 124101, 4 pages (2006).
T. Kapitula, P.G. Kevrekidis and Z. Chen, Three is a crowd: Solitary Waves in Photorefractive Media with Three Potential Wells, SIAM Journal of Applied Dynamical Systems 5, 598-633 (2006).
M. Centurion, M.A. Porter, Ye Pu, P.G. Kevrekidis, D.J. Frantzeskakis and D. Psaltis, Modulational Instability in a Layered Kerr Medium: Theory and Experiment, Phys. Rev. Lett. 97, 234101, 4 pages (2006).