Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 30 of 70
Full-Text Articles in Physical Sciences and Mathematics
When Does Linear Stability Not Exclude Nonlinear Instability?, Panos Kevrekidis, D. E. Pelinovsky, A. Saxena
When Does Linear Stability Not Exclude Nonlinear Instability?, Panos Kevrekidis, D. E. Pelinovsky, A. Saxena
Panos Kevrekidis
We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization’s internal modes of negative energy with the continuous spectrum. In a broad class of nonlinear Schrödinger equations considered, the presence of such internal modes guarantees the nonlinear instability of the stationary states in the evolution dynamics. To corroborate this idea, we explore three prototypical case examples: (a) an antisymmetric soliton in a double-well potential, (b) a twisted localized mode in a one-dimensional lattice with cubic …
Stability And Tunneling Dynamics Of A Dark-Bright Soliton Pair In A Harmonic Trap, E. T. Karamatskos, J. Stockhofe, Panos Kevrekidis, P. Schmelcher
Stability And Tunneling Dynamics Of A Dark-Bright Soliton Pair In A Harmonic Trap, E. T. Karamatskos, J. Stockhofe, Panos Kevrekidis, P. Schmelcher
Panos Kevrekidis
http://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.043637
Highly Nonlinear Wave Propagation In Elastic Woodpile Periodic Structures, Panos Kevrekidis
Highly Nonlinear Wave Propagation In Elastic Woodpile Periodic Structures, Panos Kevrekidis
Panos Kevrekidis
In the present work, we experimentally implement, numerically compute with, and theoretically analyze a configuration in the form of a single column woodpile periodic structure. Our main finding is that a Hertzian, locally resonant, woodpile lattice offers a test bed for the formation of genuinely traveling waves composed of a strongly localized solitary wave on top of a small amplitude oscillatory tail. This type of wave, called a nanopteron, is not only motivated theoretically and numerically, but is also visualized experimentally by means of a laser Doppler vibrometer. This system can also be useful for manipulating stress waves at will, …
Dark-Bright Solitons And Their Lattices In Atomic Bose-Einstein Condensates, D. Yan, F. Tsitoura, Panos Kevrekidis, D. J. Frantzeskakis
Dark-Bright Solitons And Their Lattices In Atomic Bose-Einstein Condensates, D. Yan, F. Tsitoura, Panos Kevrekidis, D. J. Frantzeskakis
Panos Kevrekidis
In the present contribution, we explore a host of different stationary states, namely dark-bright solitons and their lattices, that arise in the context of multicomponent atomic Bose-Einstein condensates. The latter are modeled by systems of coupled Gross-Pitaevskii equations with general interaction (nonlinearity) coefficients gij. It is found that in some particular parameter ranges such solutions can be obtained in analytical form, however, numerically they are computed as existing in a far wider parametric range. Many features of the solutions under study, such as their analytical form without the trap or the stability and dynamical properties of one dark-bright soliton even …
Transitions From Order To Disorder In Multi-Dark And Multi-Dark-Bright Soliton Atomic Clouds, Wenlong Wang, Panos Kevrekidis
Transitions From Order To Disorder In Multi-Dark And Multi-Dark-Bright Soliton Atomic Clouds, Wenlong Wang, Panos Kevrekidis
Panos Kevrekidis
We have performed a systematic study quantifying the variation of solitary wave behavior from that of an ordered cloud resembling a “crystalline” configuration to that of a disordered state that can be characterized as a soliton “gas.” As our illustrative examples, we use both one-component, as well as two-component, one-dimensional atomic gases very close to zero temperature, where in the presence of repulsive interatomic interactions and of a parabolic trap, a cloud of dark (dark-bright) solitons can form in the one- (two-) component system. We corroborate our findings through three distinct types of approaches, namely a Gross-Pitaevskii type of partial …
Dynamics Of Vortex Dipoles In Anisotropic Bose-Einstein Condensates, Roy H. Goodman, Panos Kevrekidis, R. Carretero-Gonzalez
Dynamics Of Vortex Dipoles In Anisotropic Bose-Einstein Condensates, Roy H. Goodman, Panos Kevrekidis, R. Carretero-Gonzalez
Panos Kevrekidis
We study the motion of a vortex dipole in a Bose--Einstein condensate confined to an anisotropic trap. We focus on a system of ODEs describing the vortices' motion, which is in turn a reduced model of the Gross--Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. We uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals in the overall direction …
Scattering Of Matter-Waves In Spatially Inhomogeneous Environments, F. Tsitoura, P. Kruger, Panos Kevrekidis, D. J. Frantzeskakis
Scattering Of Matter-Waves In Spatially Inhomogeneous Environments, F. Tsitoura, P. Kruger, Panos Kevrekidis, D. J. Frantzeskakis
Panos Kevrekidis
We study scattering of quasi-one-dimensional matter waves at an interface of two spatial domains, one with repulsive and one with attractive interatomic interactions. It is shown that the incidence of a Gaussian wave packet from the repulsive to the attractive region gives rise to generation of a soliton train. More specifically, the number of emergent solitons can be controlled, e.g., by the variation of the amplitude or the width of the incoming wave packet. Furthermore, we study the reflectivity of a soliton incident from the attractive region to the repulsive one. We find the reflection coefficient numerically and employ analytical …
Solitons And Vortices In Two-Dimensional Discrete Nonlinear Schrodinger Systems With Spatially Modulated Nonlinearity, Panos Kevrekidis
Solitons And Vortices In Two-Dimensional Discrete Nonlinear Schrodinger Systems With Spatially Modulated Nonlinearity, Panos Kevrekidis
Panos Kevrekidis
We consider a two-dimensional (2D) generalization of a recently proposed model [Gligorić et al., Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the center to the periphery. We explore the 2D model starting from the anticontinuum (AC) limit of vanishing coupling. In this limit, we can construct a wide variety of solutions including not only single-site excitations, but also dipole and quadrupole ones. Additionally, two separate families of solutions are explored: the usual “extended” unstaggered bright solitons, in which all sites are excited in the …
A Mean-Field Analogue Of The Hong-Ou-Mandel Experiment With Bright Solitons, Zhi-Yuan Sun, Panos Kevrekidis, Peter Kruger
A Mean-Field Analogue Of The Hong-Ou-Mandel Experiment With Bright Solitons, Zhi-Yuan Sun, Panos Kevrekidis, Peter Kruger
Panos Kevrekidis
In the present work, we theoretically propose and numerically illustrate a mean-field analog of the Hong-Ou-Mandel experiment with bright solitons. More specifically, we scatter two solitons off of each other (in our setup, the bright solitons play the role of a classical analog to the quantum photons of the original experiment), while the role of the beam splitter is played by a repulsive Gaussian barrier. In our classical scenario, distinguishability of the particles yields, as expected, a 0.5 split mass on either side. Nevertheless, for very slight deviations from the completely symmetric scenario, a near-perfect transmission can be constructed instead, …
A Tale Of Two Distributions: From Few To Many Vortices In Quasi-Two-Dimensional Bose-Einstein Condensates, T. Kolokolnikov, Panos Kevrekidis, R. Carretero-Gonzalez
A Tale Of Two Distributions: From Few To Many Vortices In Quasi-Two-Dimensional Bose-Einstein Condensates, T. Kolokolnikov, Panos Kevrekidis, R. Carretero-Gonzalez
Panos Kevrekidis
Motivated by the recent successes of particle models in capturing the precession and interactions of vortex structures in quasi-two-dimensional Bose–Einstein condensates, we revisit the relevant systems of ordinary differential equations. We consider the number of vortices N as a parameter and explore the prototypical configurations (‘ground states’) that arise in the case of few or many vortices. In the case of few vortices, we modify the classical result illustrating that vortex polygons in the form of a ring are unstable for N≥7. Additionally, we reconcile this modification with the recent identification of symmetry-breaking bifurcations for the cases of N=2,…,5. We …
Dynamic And Energetic Stabilization Of Persistent Currents In Bose-Einstein Condensates, K.J. H. Law, T. W. Neely, Panos Kevrekidis, B. P. Anderson, A. S. Bradley, R. Carretero-Gonzalez
Dynamic And Energetic Stabilization Of Persistent Currents In Bose-Einstein Condensates, K.J. H. Law, T. W. Neely, Panos Kevrekidis, B. P. Anderson, A. S. Bradley, R. Carretero-Gonzalez
Panos Kevrekidis
We study conditions under which vortices in a highly oblate harmonically trapped Bose-Einstein condensate (BEC) can be stabilized due to pinning by a blue-detuned Gaussian laser beam, with particular emphasis on the potentially destabilizing effects of laser beam positioning within the BEC. Our approach involves theoretical and numerical exploration of dynamically and energetically stable pinning of vortices with winding number up to S=6, in correspondence with experimental observations. Stable pinning is quantified theoretically via Bogoliubov-de Gennes excitation spectrum computations and confirmed via direct numerical simulations for a range of conditions similar to those of experimental observations. The theoretical and numerical …
Exploring Vortex Dynamics In The Presence Of Dissipation: Analytical And Numerical Results, D. Yan, R. Carretero-Gonzalez, D. J. Frantzeskakis, Panos Kevrekidis, N. P. Proukakis, D. Spirn
Exploring Vortex Dynamics In The Presence Of Dissipation: Analytical And Numerical Results, D. Yan, R. Carretero-Gonzalez, D. J. Frantzeskakis, Panos Kevrekidis, N. P. Proukakis, D. Spirn
Panos Kevrekidis
In this paper, we examine the dynamical properties of vortices in atomic Bose-Einstein condensates in the presence of phenomenological dissipation, used as a basic model for the effect of finite temperatures. In the context of this so-called dissipative Gross-Pitaevskii model, we derive analytical results for the motion of single vortices and, importantly, for vortex dipoles, which have become very relevant experimentally. Our analytical results are shown to compare favorably to the full numerical solution of the dissipative Gross-Pitaevskii equation where appropriate. We also present results on the stability of vortices and vortex dipoles, revealing good agreement between numerical and analytical …
Scattering And Leapfrogging Of Vortex Rings In A Superfluid, R. M. Caplan, J. D. Talley, R. Carretero-Gonzalez, Panos Kevrekidis
Scattering And Leapfrogging Of Vortex Rings In A Superfluid, R. M. Caplan, J. D. Talley, R. Carretero-Gonzalez, Panos Kevrekidis
Panos Kevrekidis
The dynamics of vortex ring pairs in the homogeneous nonlinear Schrödinger equation is studied. The generation of numerically exact solutions of traveling vortex rings is described and their translational velocity compared to revised analytic approximations. The scattering behavior of co-axial vortex rings with opposite charge undergoing collision is numerically investigated for different scattering angles yielding a surprisingly simple result for its dependence as a function of the initial vortex ring parameters. We also study the leapfrogging behavior of co-axial rings with equal charge and compare it with the dynamics stemming from a modified version of the reduced equations of motion …
From Nodeless States And Vortices To Gray Rings And Symmetry-Broken States In Two-Dimensional Polariton Condensates, A. S. Rodrigues, Panos Kevrekidis, R. Carretero-Gonzalez, J. Cuevas, D. J. Frantzeskakis, F. Palermo
From Nodeless States And Vortices To Gray Rings And Symmetry-Broken States In Two-Dimensional Polariton Condensates, A. S. Rodrigues, Panos Kevrekidis, R. Carretero-Gonzalez, J. Cuevas, D. J. Frantzeskakis, F. Palermo
Panos Kevrekidis
We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of interesting features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose–Einstein condensates (BECs). For sizeable parameter ranges, in line with earlier findings, the nodeless state becomes unstable towards the formation of stable nonlinear single or multi-vortex excitations. The potential instability of the single vortex is also examined and is found to possess similar characteristics to those of the …
Beating Dark-Dark Solitons And Zitterbewegung In Spin-Orbit Coupled Bose-Einstein Condensates, V. Achilleos, D. J. Frantzeskakis, Panos Kevrekidis
Beating Dark-Dark Solitons And Zitterbewegung In Spin-Orbit Coupled Bose-Einstein Condensates, V. Achilleos, D. J. Frantzeskakis, Panos Kevrekidis
Panos Kevrekidis
We present families of beating dark-dark solitons in spin-orbit (SO) -coupled Bose-Einstein condensates. These families consist of solitons residing simultaneously in the two bands of the energy spectrum. The soliton components are characterized by two different spatial and temporal scales, which are identified by a multiscale expansion method. The solitons are “beating” ones, as they perform density oscillations. The characteristic frequency of the latter is relevant to Zitterbewegung (ZB) oscillations, which were recently observed in experiments with SO-coupled condensates [C. Qu et al., Phys. Rev. A 88, 021604(R) (2013); L. J. LeBlanc et al., New J. Phys. 15, 073011 (2013)]. …
Directed Ratchet Transport In Granular Chains, V. Berardi, J. Lydon, Panos Kevrekidis, C. Daraio, R. Carretero-Gonzalez
Directed Ratchet Transport In Granular Chains, V. Berardi, J. Lydon, Panos Kevrekidis, C. Daraio, R. Carretero-Gonzalez
Panos Kevrekidis
Directed-ratchet transport (DRT) in a one-dimensional lattice of spherical beads, which serves as a prototype for granular chains, is investigated. We consider a system where the trajectory of the central bead is prescribed by a biharmonic forcing function with broken time-reversal symmetry. By comparing the mean integrated force of beads equidistant from the forcing bead, two distinct types of directed transport can be observed—spatial and temporal DRT. Based on the value of the frequency of the forcing function relative to the cutoff frequency, the system can be categorized by the presence and magnitude of each type of DRT. Furthermore, we …
Multibreathers In Klein-Gordon Chains With Interactions Beyond Nearest Neighbors, V. Koukouloyannis, Panos Kevrekidis, J. Cuevas, V. Rothos
Multibreathers In Klein-Gordon Chains With Interactions Beyond Nearest Neighbors, V. Koukouloyannis, Panos Kevrekidis, J. Cuevas, V. Rothos
Panos Kevrekidis
We study the existence and stability of multibreathers in Klein-Gordon chains with interactions that are not restricted to nearest neighbors. We provide a general framework where such long range effects can be taken into consideration for arbitrarily varying (as a function of the node distance) linear couplings between arbitrary sets of neighbors in the chain. By examining special case examples such as three-site breathers with next-nearest-neighbors, we find crucial modifications to the nearest-neighbor picture of one-dimensional oscillators being excited either in- or anti-phase. Configurations with nontrivial phase profiles emerge from or collide with the ones with standard phase difference profiles, …
Statics And Dynamics Of Atomic Dark-Bright Solitons In The Presence Of Impurities, V. Achilleos, Panos Kevrekidis, V. M. Rothos, D. J. Frantzeskakis
Statics And Dynamics Of Atomic Dark-Bright Solitons In The Presence Of Impurities, V. Achilleos, Panos Kevrekidis, V. M. Rothos, D. J. Frantzeskakis
Panos Kevrekidis
Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the statics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an equation of motion for the dark-bright soliton center. We show that, counterintuitively, an attractive (repulsive) delta-like impurity, acting solely on the bright-soliton component, induces an effective localized barrier (well) in the effective potential felt by the soliton; this way, dark-bright solitons are reflected from (transmitted through) attractive (repulsive) impurities. Our analytical results for the small-amplitude oscillations of solitons are found to be in good agreement with results …
Transfer And Scattering Of Wave Packets By A Nonlinear Trap, Kai Li, Panos Kevrekidis, Boris A. Malomed, D. J. Frantzeskakis
Transfer And Scattering Of Wave Packets By A Nonlinear Trap, Kai Li, Panos Kevrekidis, Boris A. Malomed, D. J. Frantzeskakis
Panos Kevrekidis
In the framework of a one-dimensional model with a tightly localized self-attractive nonlinearity, we study the formation and transfer (dragging) of a trapped mode by “nonlinear tweezers,” as well as the scattering of coherent linear wave packets on the stationary localized nonlinearity. The use of a nonlinear trap for dragging allows one to pick up and transfer the relevant structures without grabbing surrounding “radiation.” A stability border for the dragged modes is identified by means of analytical estimates and systematic simulations. In the framework of the scattering problem, the shares of trapped, reflected, and transmitted wave fields are found. Quasi-Airy …
Vortex–Bright-Soliton Dipoles: Bifurcations, Symmetry Breaking, And Soliton Tunneling In A Vortex-Induced Double Well, M. Pola, J. Stockhofe, P. Schmelcher, Panos Kevrekidis
Vortex–Bright-Soliton Dipoles: Bifurcations, Symmetry Breaking, And Soliton Tunneling In A Vortex-Induced Double Well, M. Pola, J. Stockhofe, P. Schmelcher, Panos Kevrekidis
Panos Kevrekidis
The emergence of vortex-bright soliton dipoles in two-component Bose-Einstein condensates through bifurcations from suitable eigenstates of the underlying linear system is examined. These dipoles can have their bright solitary structures be in phase (symmetric) or out of phase (anti-symmetric). The dynamical robustness of each of these two possibilities is considered and the out-of-phase case is found to exhibit an intriguing symmetry-breaking instability that can in turn lead to tunneling of the brightwave function between the two vortex “wells.” We interpret this phenomenon by virtue of a vortex-induced double-well system, whose spontaneous symmetry breaking leads to asymmetric vortex-bright dipoles, in addition …
Nonlinear Pt-Symmetric Plaquettes, Kai Li, Panos Kevrekidis, Boris A. Malomed, Uwe Günther
Nonlinear Pt-Symmetric Plaquettes, Kai Li, Panos Kevrekidis, Boris A. Malomed, Uwe Günther
Panos Kevrekidis
We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its PT symmetry. The corresponding nonlinear modes are analyzed starting from the Hamiltonian limit, with zero value of the gain-loss coefficient, . Once the relevant waveforms have been identified (chiefly, in an analytical form), their stability is examined by means of linearization in the vicinity of stationary points. This reveals diverse and, occasionally, fairly complex bifurcations. The evolution of unstable modes is explored by means of …
Finite-Temperature Dynamics Of Matter-Wave Dark Solitons In Linear And Periodic Potentials: An Example Of An Antidamped Josephson Junction, Y. Shen, Panos Kevrekidis, N. Whitaker, N. I. Karachalios, D. J. Frantzeskakis
Finite-Temperature Dynamics Of Matter-Wave Dark Solitons In Linear And Periodic Potentials: An Example Of An Antidamped Josephson Junction, Y. Shen, Panos Kevrekidis, N. Whitaker, N. I. Karachalios, D. J. Frantzeskakis
Panos Kevrekidis
We study matter-wave dark solitons in atomic Bose-Einstein condensates (BECs) at finite temperatures, under the effect of linear and periodic potentials. Our model, namely, a dissipative Gross-Pitaevskii equation, is treated analytically by means of dark-soliton perturbation theory and the Landau dynamics approach, which result in a Newtonian equation of motion for the dark-soliton center. This reduced model, which incorporates an effective washboard potential and an antidamping term accounting for finite-temperature effects, constitutes an example of an antidamped Josephson junction. We perform a qualitative (local and global) analysis of the equation of motion. We present results of systematic numerical simulations for …
Ultrashort Pulses And Short-Pulse Equations In 2+1 Dimensions, Y. Shen, N. Whitaker, Panos Kevrekidis, N. L. Tsitsas, D. J. Frantzeskakis
Ultrashort Pulses And Short-Pulse Equations In 2+1 Dimensions, Y. Shen, N. Whitaker, Panos Kevrekidis, N. L. Tsitsas, D. J. Frantzeskakis
Panos Kevrekidis
In this paper, we derive and study two versions of the short pulse equation (SPE) in (2 + 1) dimensions. Using Maxwell’s equations as a starting point, and suitable Kramers-Kronig formulas for the permittivity and permeability of the medium, which are relevant, e.g., to left-handed metamaterials and dielectric slab wave guides, we employ a multiple scales technique to obtain the relevant models. General properties of the resulting (2 + 1)-dimensional SPEs, including fundamental conservation laws, as well as the Lagrangian and Hamiltonian structure and numerical simulations for one- and two-dimensional initial data, are presented. Ultrashort one-dimensional breathers appear to be …
Dark Solitons And Vortices In Pt-Symmetric Nonlinear Media: From Spontaneous Symmetry Breaking To Nonlinear Pt Phase Transitions, V. Achilleos, Panos Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonz´Alez
Dark Solitons And Vortices In Pt-Symmetric Nonlinear Media: From Spontaneous Symmetry Breaking To Nonlinear Pt Phase Transitions, V. Achilleos, Panos Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonz´Alez
Panos Kevrekidis
We consider nonlinear analogs of parity-time- (PT-) symmetric linear systems exhibiting defocusing nonlinearities. We study the ground state and odd excited states (dark solitons and vortices) of the system and report the following remarkable features. For relatively weak values of the parameter ɛ controlling the strength of the PT-symmetric potential, excited states undergo (analytically tractable) spontaneous symmetry breaking; as ɛ is further increased, the ground state and first excited state, as well as branches of higher multisoliton (multivortex) states, collide in pairs and disappear in blue-sky bifurcations, in a way which is strongly reminiscent of the linear PT phase transition—thus …
Dark Lattice Solitons In One-Dimensional Waveguide Arrays With Defocusing Saturable Nonlinearities And Alternating Couplings, Andrey Kanshu, Christian E. Rüter, Detlef Kip, Jesús Cuevas, Panos Kevrekidis
Dark Lattice Solitons In One-Dimensional Waveguide Arrays With Defocusing Saturable Nonlinearities And Alternating Couplings, Andrey Kanshu, Christian E. Rüter, Detlef Kip, Jesús Cuevas, Panos Kevrekidis
Panos Kevrekidis
In the present work, we examine "binary" waveguide arrays, where the coupling between adjacent sites alternates between two distinct values $C_1$ and $C_2$ and a saturable nonlinearity is present on each site. Motivated by experimental investigations of this type of system in fabricated LiNbO$_3$ arrays, we proceed to analyze the nonlinear wave excitations arising in the self-defocusing nonlinear regime, examining, in particular, dark solitons and bubbles. We find that such solutions may, in fact, possess a reasonably wide, experimentally relevant parametric interval of stability, while they may also feature both prototypical types of instabilities, namely exponential and oscillatory ones, for …
Dark-Bright Solitons In Bose–Einstein Condensates At Finite Temperatures, V. Achilleos, D. Yan, Panos Kevrekidis, D. J. Frantzeskakis
Dark-Bright Solitons In Bose–Einstein Condensates At Finite Temperatures, V. Achilleos, D. Yan, Panos Kevrekidis, D. J. Frantzeskakis
Panos Kevrekidis
We study the dynamics of dark-bright (DB) solitons in binary mixtures of Bose gases at finite temperature using a system of two coupled dissipative Gross–Pitaevskii equations. We develop a perturbation theory for the two-component system to derive an equation of motion for the soliton centers and identify different temperature-dependent damping regimes. We show that the effect of the bright ('filling') soliton component is to partially stabilize 'bare' dark solitons against temperature-induced dissipation, thus providing longer lifetimes. We also study analytically thermal effects on DB soliton 'molecules' (i.e. two in-phase and out-of-phase DB solitons), showing that they undergo expanding oscillations while …
Dynamics Of Bright Solitons And Soliton Arrays In The Nonlinear Schrödinger Equation With A Combination Of Random And Harmonic Potentials, Qian-Yong Chen, Panos Kevrekidis, Boris A. Malomed
Dynamics Of Bright Solitons And Soliton Arrays In The Nonlinear Schrödinger Equation With A Combination Of Random And Harmonic Potentials, Qian-Yong Chen, Panos Kevrekidis, Boris A. Malomed
Panos Kevrekidis
We report results of systematic simulations of the dynamics of solitons in the framework of the one-dimensional nonlinear Schrödinger equation, which includes the harmonic oscillator potential and a random potential. The equation models experimentally relevant spatially disordered settings in Bose–Einstein condensates (BECs) and nonlinear optics. First, the generation of soliton arrays from a broad initial quasi-uniform state by the modulational instability (MI) is considered following a sudden switch of the nonlinearity from repulsive to attractive. Then, we study oscillations of a single soliton in this setting, which models a recently conducted experiment in a BEC. The basic characteristics of the …
Defect Modes In One-Dimensional Granular Crystals, Y. Man, N. Boechler, G. Theocharis, Panos Kevrekidis, C. Daraio
Defect Modes In One-Dimensional Granular Crystals, Y. Man, N. Boechler, G. Theocharis, Panos Kevrekidis, C. Daraio
Panos Kevrekidis
We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing light-mass defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uniform spherical particles. We present a systematic measurement, using continuous noise, of the near-linear frequency spectrum within the spatial vicinity of the defect(s). Using this technique, we identify the frequencies of the localized defect modes as a function of the defect size and the position of the defects relative to each other. We also compare the experimentally determined …
Spatial Solitons Under Competing Linear And Nonlinear Diffractions, Y. Shen, Panos Kevrekidis, N. Whitaker
Spatial Solitons Under Competing Linear And Nonlinear Diffractions, Y. Shen, Panos Kevrekidis, N. Whitaker
Panos Kevrekidis
We introduce a general model which augments the one-dimensional nonlinear Schrödinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a Hamiltonian representation in a form natural for optical media. The equation serves as a model for spatial solitons near the supercollimation point in nonlinear photonic crystals. In the framework of this model, a detailed analysis of the fundamental solitary waves is reported, including the variational approximation (VA), exact analytical results, and systematic numerical computations. The Vakhitov-Kolokolov (VK) criterion is used to precisely predict the stability border for the solitons, …
Escape Dynamics In The Discrete Repulsive Model, V. Achilleos, A. Alvarez, J. Cuevas, D. J. Frantzeskakis, N. I. Karachalios, Panos Kevrekidis, B. Sanchez-Rey
Escape Dynamics In The Discrete Repulsive Model, V. Achilleos, A. Alvarez, J. Cuevas, D. J. Frantzeskakis, N. I. Karachalios, Panos Kevrekidis, B. Sanchez-Rey
Panos Kevrekidis
We study deterministic escape dynamics of the discrete Klein-Gordon model with a repulsive quartic on-site potential. Using a combination of analytical techniques, based on differential and algebraic inequalities and selected numerical illustrations, we first derive conditions for collapse of an initially excited single-site unit, for both the Hamiltonian and the linearly damped versions of the system and showcase different potential fates of the single-site excitation, such as the possibility to be “pulled back” from outside the well or to “drive over” the barrier some of its neighbors. Next, we study the evolution of a uniform (small) segment of the chain …