Fractional Dispersive Models and Applications

Prof. Panayotis Kevrekidis earned his B.Sc. Degree from the University of Athens (1996) and a M.S. (1998), an M.Phil. (2000) and a Ph.D. (2000) in Physics from Rutgers University. He then spent a postdoctoral research year split between the PACM in Princeton and CNLS at Los Alamos National Laboratory. He joined the Department of Mathematics and Statistics of UMass, Amherst, as an Assistant Professor in September 2001. He became Associate Professor in 2005, Full Professor in 2010 and a Distinguished University Professor in 2015. Kevrekidis' interests are centered around the nonlinear dynamics of solitary waves in nonlinear partial differential equations and in lattice nonlinear differential-difference equations and the properties (existence, stability, dynamics) of such waves. A focal point of this work concerns the applications of such tools and techniques to systems from Physics (especially nonlinear optics and atomic physics), Materials Science, Biology and Chemistry. He has published over 700 research papers in a wide variety of venues in nonlinear physics and applied mathematics, given over 200 research lectures in conferences and universities around the globe, is an associate editor of 3 journals and has authored 8 books.As quantitative measures of Kevrekidis’ impact to the research community, one can mention the h-index of 65 (in Web of Science, 82 in Google Scholar) and that his work has been cited over 28500 times (according to Google Scholar).Prof. Jesús Cuevas-Maraver earned his B.Sc. Degree from the Faculty of Physics of the University of Seville in 1999 graduating third with a GPA of 7.87/10.0. He subsequently joined the Department of Applied Physics I of the same university where obtained his Ph.D. in Physics in 2003 under the supervision of Prof. Francisco R. Romero and Prof. Juan F.R. Archilla, with a Ph.D. thesis entitled “Localization and energy transfer in nonlinear inhomogenous systems”. After that, he joined the same department as an Assistant Professor and, from 2009, he is Associate Professor therein. His lectures in Elementary Physics (Mechanics, Thermodynamics and Electromagnetism) and Thermal Hydraulics take place at the Polytechnic School in several degrees of Industrial Engineering.His research covers many aspects of Nonlinear Science and is based in the theoretical study of nonlinear localized waves as solitons, kinks or breathers that emerge in many physics systems. He has considered a wide range of such systems, which includes crystals, biomolecules, Bose–Einstein condensates, waveguide arrays, nonlinear circuits or transmission lines and metamaterials. He is a frequent referee in international journals, including Nature Physics, Physical Review Letters or Optics Letters. Prof. Jesús Cuevas-Maraver has written 134 scientific publications covering international journals and books. He has also edited 5 books.As quantitative measures of Cuevas-Maraver’s impact to the research community, one can mention the h-index of 27 in Web of Science (35 in Google Scholar) and that his work has been cited over 2000 times, according to Web of Science (over 3000 in Google Scholar).

• Chapter 1. Fractional Dispersive Models and Applications (Panayotis G. Kevrekidis).- Chapter 2. Fractional Wave Models and Their Experimental Applications (Boris A. Malomed).- Chapter 3. Fractional Models in Biology and Medicine (Fractional Models in Biology and Medicine).- Chapter 4. Fractional Dissipative PDEs (Franz Achleitner).- Chapter 5. Symmetry breaking in fractional nonlinear Schrödinger and soliton dynamics in complex Ginzburg-Landau models (Pengfei Li).- Chapter 6. Traveling waves in fractional models (Traveling waves in fractional models).- Chapter 7. Numerical methods for fractional PDEs (Christian Klein).- Chapter 8. Fractional Non-Linear Quantum Analysis, Probability, Discretization, and Limits (Kay L. Kirkpatrick).- Chapter 9. Fractional Integrable Dispersive Equations (Mark J. Ablowitz).- Chapter 10. Fractional discrete linear and nonlinear models (Mario I. Molina).- Chapter 11. Breathers in the fractionalFrenkel-Kontorova model (J. Catarecha).