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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 …