In refereed Journals:
J-6 Yannan Shen, P. G. Kevrekidis, G. P. Veldes, D. J. Frantzeskakis, D. DiMarzio, X. Lan, and V. Radisic, From solitons to rogue waves in nonlinear left-handed metamaterials, Phys. Rev. E 95, 032223 (2017).
Περίληψη/Abstract: In the present work, we explore soliton and rogue like wave solutions in the transmission line analog of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltage-dependent, symmetric capacitance motivated by recently developed ferroelectric barium strontium titanate thin-film capacitor designs. We develop both the corresponding nonlinear dynamical lattice and its reduction via a multiple scales expansion to a nonlinear Schrodinger (NLS) model for the envelope of a given carrier wave. The reduced model can feature either a focusing or a defocusing nonlinearity depending on the frequency (wave number) of the carrier. We then consider the robustness of different types of solitary waves of the reduced model within the original nonlinear left-handed medium. We find that both bright and dark solitons persist in a suitable parametric regime, where the reduction to the NLS model is valid. Additionally, for suitable initial conditions, we observe a rogue wave type of behavior that differs significantly from the classic Peregrine rogue wave evolution, including most notably the breakup of a single Peregrine-like pattern into solutions with multiple wave peaks. Finally, we touch upon the behavior of generalized members of the family of the Peregrine solitons, namely, Akhmediev breathers and Kuznetsov-Ma solitons, and explore how these evolve in the left-handed transmission line.
J-5 M. Agaoglou, V. M. Rothos, D. J. Frantzeskakis, G. P. Veldes, and H. Susanto, Bifurcation results for travelling waves in nonlinear magnetic metamaterials, International Journal of Bifurcation and Chaos 24, 1450147 (2014).
Περίληψη/Abstract: In this work, we study a model of a one-dimensional magnetic metamaterial formed by a discrete array of nonlinear resonators. We focus on periodic and localized traveling waves of the model, in the presence of loss and an external drive. Employing a Melnikov analysis we study the existence and persistence of such traveling waves, and study their linear stability. We show that, under certain conditions, the presence of dissipation and/or driving may stabilize or destabilize the solutions. Our analytical results are found to be in good agreement with direct numerical computations.
J-4 G. P. Veldes, J. Cuevas,P. G.Kevrekidis, and D. J. Frantzeskakis, Coupled backward- and forward-propagating solitons in a composite right- and left-handed transmission line Phys. Rev.E 88, 013203 (2013).
Περίληψη/Abstract: We study the coupling between backward- and forward-propagating wave modes, with the same group velocity, in a composite right/left-handed nonlinear transmission line. Using an asymptotic multiscale expansion technique, we derive a system of two coupled nonlinear Schrodinger equations governing the evolution of the envelopes of these modes. We show that this system supports a variety of backward- and forward propagating vector solitons, of the bright-bright, bright-dark and dark-bright type. Performing systematic numerical simulations in the framework of the original lattice that models the transmission line, we study the propagation properties of the derived vector soliton solutions. We show that all types of the predicted solitons exist, but differ on their robustness: only bright-bright solitons propagate undistorted for long times, while the other types are less robust, featuring shorter lifetimes. In all cases, our analytical predictions are in a very good agreement with the results of the simulations, at least up to times of the order of the solitons’ lifetimes.
J-3 G.P. Veldes, J. Borhanian, M. McKerr, V. Saxena, D.J. Frantzeskakis and I. Kourakis, Electromagnetic Rogue Waves in Beam-Plasma Interactions, J. Opt. 15, 064003 (2013) /Journal of Optics “Highlights of 2013”.
Περίληψη/Abstract: The occurrence of rogue waves (freak waves) associated with electromagnetic pulse propagation interacting with a plasma is investigated, from first principles. A multiscale technique is employed to solve the fluid-Maxwell equations describing a weakly nonlinear circularly polarized electromagnetic pulses in magnetized plasmas. A nonlinear Schrodinger (NLS) type equation is shown to govern the amplitude of the vector potential. A set of non-stationary envelope solutions of the NLS equation are considered, as potential candidates for modeling of rogue waves (freak waves) in beam-plasma interactions, namely in the form of the Peregrine soliton, the Akhmediev breather and the Kuznetsov-Ma breather. The variation of the structural properties of the latter structures with relevant plasma parameters is investigated, in particular focusing on the ratio between the (magnetic field dependent) cyclotron (gyro-) frequency and the plasma frequency.
loPLabTalk article (online, 2013):“Monster waves in a laser beam: myth or reality?”( http://iopscience.iop.org/2040-8986/labtalk-article/53714).
J-2 G. P. Veldes, J. Cuevas,P. G.Kevrekidis, and D. J. Frantzeskakis, Quasidiscrete microwave solitons in a split-ring-resonator-based left-handed coplanar waveguide, Phys. Rev. E 83, 046608 (2011).
Περίληψη/Abstract: We study the propagation of quasidiscrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split-ring resonators. By considering the relevant transmission line analog, we derive a nonlinear lattice model which is studied analytically by means of a quasidiscrete approximation. We derive a nonlinear Schrodinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the propagation properties of the quasidiscrete microwave solitons. Our numerical findings are in good agreement with the analytical predictions, and suggest that the predicted structures are quite robust and may be observed in experiments.
J-1 L. Q. English, S. G. Wheeler, Y. Shen, G. P. Veldes, N.Whitaker,P. G.Kevrekidis, and D. J.Frantzeskakis, Backward-wave propagation and discrete solitons in a left-handed electrical lattice, Phys. Lett.A 375, 1242 (2011).
Περίληψη/Abstract: We study experimentally, analytically and numerically the backward-wave propagation, and formation of discrete bright and dark solitons in a nonlinear electrical lattice. We observe experimentally that a focusing (defocusing) effect occurs above (below) a certain carrier frequency threshold, and backwardpropagating bright (dark) discrete solitons are formed. We develop a discrete model emulating the relevant circuit and benchmark its linear properties against the experimental dispersion relation. Using a perturbation method, we derive a nonlinear Schrödinger equation, that predicts accurately the carrier frequency threshold. Finally, we use numerical simulations to corroborate our findings and monitor the space–time evolution of the discrete solitons.
C-1 “Rogue Waves Associated with Circularly Polarized Waves in Magnetized Plasmas” Kourakis, I.; Borhanian, J.; Saxena, V.; Veldes, G. P.; Frantzeskakis, D. J. American Physical Society, 54th Annual Meeting of the APS Division of Plasma Physics, October 29-November 2, 2012.
W-1 “Dynamics in Samos – Workshop on Differential Equations, Dynamical Systems and Applications” Samos, Greece, 31 August-3 September 2010.