
Panayotis G. Kevrekidis, Professor 



Office  LGRT 1524

Phone  (413) 5771977

Fax  (413) 5451801 
Email  kevrekid <at> math.umass.edu 

Mailing Address 
 Department of Mathematics and Statistics 
Lederle Graduate Research Tower 
University of Massachusetts 
Amherst, MA 010039305 



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 softcondensed matter setting of BoseEinstein Condensates. The research mainly revolves around the existence, stability and dynamics of localized (solitary wave) structures in such one, two and threedimensional setups, often described by equations of Nonlinear Schrodinger or KleinGordon type. While the settings under study are principally Hamiltonian in nature (often featuring external potentials, or being genuinely discrete and posed on, socalled, 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 reactiondiffusion models, and dynamics and energy landscapes of glassy materials among others. 

Current Teaching: Math 534H, Spring 2016 

Previous Teaching 

Math 691Y, Applied Math, M.S. Project, Fall 2013 

Math 532H, Dynamical Systems with Applications in
Physics, Chemistry and Biology,
Fall 13 

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 597697Y, 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 06Spring 07 (cotaught with N. Whitaker) 

Math 534, Introduction to Partial Differential Equations,
Spring 06 

Math 132, Calculus II, Course Chair and Sections 45, 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, 212232 (2000) 

P.G. Kevrekidis and M.I. Weinstein, Dynamics of Lattice Kinks, Physica 142D, 113152 (2000) 

T. Kapitula and P. Kevrekidis, Stability of Waves in Discrete Systems, Nonlinearity 14, 533566 (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, 28332900 (2001). 

A. Smerzi, A. Trombettoni, P.G. Kevrekidis and A.R. Bishop, SuperfluidInsulator Transition in a Chain of Weakly Coupled BoseEinstein 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, 497506 (2003). 

P.G. Kevrekidis, G. Theocharis, D.J. Frantzeskakis, and Boris A. Malomed, Feshbach Resonance Management for BoseEinstein Condensates, Phys. Rev. Lett. 90, 230401 (2003). 

T.Kapitula, P.G. Kevrekidis and B. Sandstede, Counting eigenvalues via the Krein signature in infinitedimensional Hamiltonian systems, Physica D 195, 263282 (2004). 

A. Stefanov and P.G. Kevrekidis, Asymptotic behavior of small solutions for the discrete nonlinear Schrodinger and KleinGordon
equations, Nonlinearity 18, 18411857 (2005). 

D.E. Pelinovsky, P.G. Kevrekidis and D.J. Frantzeskakis, Stability of discrete solitons in Nonlinear Schrodinger Lattices, Physica D 212, 119 (2005). 

D.E. Pelinovsky, P.G. Kevrekidis and D.J. Frantzeskakis, Persistence and stability of discrete vortices in nonlinear Schrodinger lattices, Physica D 212, 2053 (2005). 

T. Kapitula and P.G. Kevrekidis, BoseEinstein Condensates in the presence of a magnetic trap and an optical lattice: twomode approximation, Nonlinearity 18, 24912512 (2005). 

X. Wang, Z. Chen and P.G. Kevrekidis, Observation of discrete solitons and soliton rotation in opticallyinduced periodic ring lattices, Phys. Rev. Lett. 96, 083904, 4 pages (2006). 

P.G. Kevrekidis and D.E. Pelinovsky, Discrete Vector onsite Vortices, Proceedings of the Royal Society of London A 462, 26712694 (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, 598633 (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). 
