Spinor Bose-Einstein condensates in double well potentials (2008)
Wang, C., Kevrekidis, P. G., Whitaker, N., Alexander, T. J., Frantzeskakis, D. J., Schmelcher, P.
We consider the statics and dynamics of F = 1 spinor Bose-Einstein condensates (BECs) confined in double well potentials. We use a two-mode Galerkin-type quasi-analytical approximation to describe...
Wave patterns generated by a supersonic moving body in a binary Bose-Einstein condensate (2008)
Gladush, Yu. G., Kamchatnov, A. M., Shi, Z., Kevrekidis, P. G., Frantzeskakis, D. J., Malomed, B. A.
Generation of wave structures by a two-dimensional object (laser beam) moving in a two-dimensional two-component Bose-Einstein condensate with a velocity greater than both sound velocities of the...
Middelkamp, S., Kevrekidis, P. G., Frantzeskakis, D. J., Schmelcher, P.
We study the dynamics of bright and dark matter-wave solitons in the presence of a spatially varying nonlinearity. When the spatial variation does not involve zero crossings, a transformation is used...
Spinor Bose-Einstein condensate flow past an obstacle (2008)
Rodrigues, A. S., Kevrekidis, P. G., Carretero-González, R., Frantzeskakis, D. J., Schmelcher, P., Alexander, T. J., ...
We study the flow of a spinor (F=1) Bose-Einstein condensate in the presence of an obstacle. We consider the cases of ferromagnetic and polar spin-dependent interactions and find that the system...
Collisionally inhomogeneous Bose-Einstein condensates in double-well potentials (2008)
Wang, C., Kevrekidis, P. G., Whitaker, N., Frantzeskakis, D. J., Schmelcher, P., Middelkamp, S.
In this work, we consider quasi-one-dimensional Bose-Einstein condensates (BECs), with spatially varying collisional interactions, trapped in double well potentials. In particular, we study a setup...
Surface Solitons in Three Dimensions (2008)
Hoq, Q. E., Carretero-Gonzalez, R., Kevrekidis, P. G., Malomed, B. A., Frantzeskakis, D. J., Bludov, Yu. V., ...
We study localized modes on the surface of a three-dimensional dynamical lattice. The stability of these structures on the surface is investigated and compared to that in the bulk of the lattice....
Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques (2008)
Carretero-Gonzalez, R., Frantzeskakis, D. J., Kevrekidis, P. G.
The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates...
Rabi switch of condensate wavefunctions in a multicomponent Bose gas (2008)
Nistazakis, H. E., Rapti, Z., Frantzeskakis, D. J., Kevrekidis, P. G., Sodano, P., Trombettoni, A.
Using a time-dependent linear (Rabi) coupling between the components of a weakly interacting multicomponent Bose-Einstein condensate (BEC), we propose a protocol for transferring the wavefunction of...
Experimental observation of oscillating and interacting matter wave dark solitons (2008)
Weller, A., Ronzheimer, J. P., Gross, C., Frantzeskakis, D. J., Theocharis, G., Kevrekidis, P. G., ...
We report on the generation, subsequent oscillation and interaction of a pair of matter wave dark solitons. These are created by releasing a Bose-Einstein condensate from a double well potential into...
Law, K. J. H., Kevrekidis, P. G., Anderson, B. P., Carretero-Gonzalez, R., Frantzeskakis, D. J.
In this work, we study pancake-shaped Bose-Einstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal...
Rabi switch of condensate wavefunctions in a multicomponent Bose gas (2008)
Nistazakis, H.E., Rapti, Z., Frantzeskakis, D.J., Kevrekidis, P.G., Sodano, P., Trombettoni, A.
Matter-wave solitons with a periodic, piecewise-constant nonlinearity (2007)
Rodrigues, A. S., Kevrekidis, P. G., Porter, Mason A., Frantzeskakis, D. J., Schmelcher, P., Bishop, A. R.
Motivated by recent proposals of ``collisionally inhomogeneous'' Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties...
Dynamics of Vortex Formation in Merging Bose-Einstein Condensate Fragments (2007)
Carretero-Gonzalez, R., Anderson, B. P., Kevrekidis, P. G., Frantzeskakis, D. J., Weiler, C. N.
We study the formation of vortices in a Bose-Einstein condensate (BEC) that has been prepared by allowing isolated and independent condensed fragments to merge together. We focus on the experimental...
Dark matter-wave solitons in the dimensionality crossover (2007)
Theocharis, G., Kevrekidis, P. G., Oberthaler, M. K., Frantzeskakis, D. J.
We consider the statics and dynamics of dark matter-wave solitons in the dimensionality crossover regime from 3D to 1D. There, using the nonpolynomial Schr\"{o}dinger mean-field model, we find that...
Radially Symmetric Nonlinear States of Harmonically Trapped Bose-Einstein Condensates (2007)
Herring, G., Carr, L. D., Carretero-Gonzalez, R., Kevrekidis, P. G., Frantzeskakis, D. J.
Starting from the spectrum of the radially symmetric quantum harmonic oscillator in two dimensions, we create a large set of nonlinear solutions. The relevant three principal branches, with $n_r=0,1$...
Law, K. J. H., Kevrekidis, P. G., Frantzeskakis, D. J., Bishop, A. R.
Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider...
Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates (2007)
Niarchou, P., Theocharis, G., Kevrekidis, P. G., Schmelcher, P., Frantzeskakis, D. J.
We investigate bright matter-wave solitons in the presence of a spatially varying nonlinearity. It is demonstrated that a translation mode is excited due to the spatial inhomogeneity and its...
Non-Equilibrium Dynamics and Superfluid Ring Excitations in Binary Bose-Einstein Condensates (2007)
Mertes, K. M., Merrill, J., Carretero-Gonzalez, R., Frantzeskakis, D. J., Kevrekidis, P. G., Hall, D. S.
We revisit a classic study [D. S. Hall {\it et al.}, Phys. Rev. Lett. {\bf 81}, 1539 (1998)] of interpenetrating Bose-Einstein condensates in the hyperfine states $\ket{F = 1, m_f = -1}\equiv\ket{1}$...
Polarized States and Domain Walls in Spinor Bose-Einstein Condensates (2007)
Nistazakis, H. E., Frantzeskakis, D. J., Kevrekidis, P. G., Malomed, B. A., Carretero-Gonzalez, R., Bishop, A. R.
We study spin-polarized states and their stability in anti-ferromagnetic states of spinor (F=1) quasi-one-dimensional Bose-Einstein condensates. Using analytical approximations and numerical methods,...
Modulational instability in nonlinearity-managed optical media (2007)
Centurion, Martin, Porter, Mason A., Pu, Ye, Kevrekidis, P. G., Frantzeskakis, D. J., Psaltis, Demetri
We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically nonlinear (Kerr) optical medium that consists of alternating layers of glass and air....
Modulated amplitude waves in collisionally inhomogeneous Bose–Einstein condensates (2007)
Porter, Mason A., Kevrekidis, P. G., Malomed, Boris A., Frantzeskakis, D. J.
We investigate the dynamics of an effectively one-dimensional Bose–Einstein condensate (BEC) with scattering length a subjected to a spatially periodic modulation, a=a(x)=a(x+L). This...
Bright-Dark Soliton Complexes in Spinor Bose-Einstein Condensates (2007)
Nistazakis, H. E., Frantzeskakis, D. J., Kevrekidis, P. G., Malomed, B. A., Carretero-Gonzalez, R.
We present bright-dark vector solitons in quasi-one-dimensional spinor (F=1) Bose-Einstein condensates. Using a multiscale expansion technique, we reduce the corresponding nonintegrable system of...
Symmetry Breaking in Linearly Coupled Dynamical Lattices (2007)
Herring, G., Kevrekidis, P. G., Malomed, B. A., Carretero-Gonzalez, R., Frantzeskakis, D. J.
We examine one- and two-dimensional (1D and 2D) models of linearly coupled lattices of the discrete-nonlinear-Schr{\"{o}}dinger type. Analyzing ground states of the systems with equal powers in the...
Herring, G., Kevrekidis, P. G., Williams, F., Christodoulakis, T., Frantzeskakis, D. J.
In this work we revisit the topic of two-dimensional Bose-Einstein condensates under the influence of time-dependent magnetic confinement and time-dependent scattering length. A moment approach...
Cerenkov-like radiation in a binary Schr{\"o}dinger flow past an obstacle (2007)
Susanto, H., Kevrekidis, P. G., Carretero-Gonzalez, R., Malomed, B. A., Frantzeskakis, D. J., Bishop, A. R.
We consider the dynamics of two coupled miscible Bose-Einstein condensates, when an obstacle is dragged through them. The existence of two different speeds of sound provides the possibility for three...
Crossover dark soliton dynamics in ultracold one-dimensional Bose gases (2007)
Frantzeskakis, D. J., Kevrekidis, P. G., Proukakis, N. P.
Ultracold confined one-dimensional atomic gases are predicted to support dark soliton solutions arising from a nonlinear Schr\"{o}dinger equation of suitable nonlinearity. In weakly-interacting (high...
Modulational instability in nonlinearity-managed optical media (2007)
Centurion, M., Porter, M. A., Pu, Y., Kevrekidis, P. G., Frantzeskakis, D. J., Psaltis, D.
Modulational Instability in a Layered Kerr Medium: Theory and Experiment (2006)
Centurion, Martin, Porter, Mason A., Pu, Ye, Kevrekidis, P. G., Frantzeskakis, D. J., Psaltis, Demetri
We present the first experimental investigation of modulational instability in a layered Kerr medium. The particularly interesting and appealing feature of our configuration, consisting of...
Fractional-period excitations in continuum periodic systems (2006)
Nistazakis, H. E., Porter, Mason A., Kevrekidis, P. G., Frantzeskakis, D. J., Nicolin, A., Chin, J. K.
We investigate the generation of fractional-period states in continuum periodic systems. As an example, we consider a Bose-Einstein condensate confined in an optical-lattice potential. We show that...
Modulational Instability in Nonlinearity-Managed Optical Media (2006)
Centurion, Martin, Porter, Mason A., Pu, Ye, Kevrekidis, P. G., Frantzeskakis, D. J., Psaltis, Demetri
We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically-nonlinear (Kerr) optical medium that consists of alternating layers of glass and air....
Vortex Structures Formed by the Interference of Sliced Condensates (2006)
Carretero-Gonzalez, R., Whitaker, N., Kevrekidis, P. G., Frantzeskakis, D. J.
We study the formation of vortices, vortex necklaces and vortex ring structures as a result of the interference of higher-dimensional Bose-Einstein condensates (BECs). This study is motivated by...
Dark Solitons in Discrete Lattices: Saturable versus Cubic Nonlinearities (2006)
Fitrakis, E. P., Kevrekidis, P. G., Susanto, H., Frantzeskakis, D. J.
In the present work, we study dark solitons in dynamical lattices with the saturable nonlinearity and compare them with those in lattices with the cubic nonlinearity. This comparison has become...
Modulational instability in a layered Kerr medium: Theory and Experiment (2006)
Centurion, Martin, Porter, Mason A., Pu, Ye, Kevrekidis, P. G., Frantzeskakis, D. J., Psaltis, Demetri
We present the first experimental investigation of modulational instability in a layered Kerr medium. The particularly interesting and appealing feature of our configuration, consisting of...
Discrete surface solitons in two dimensions (2006)
Susanto, H., Kevrekidis, P. G., Malomed, B. A., Carretero-Gonzalez, R., Frantzeskakis, D. J.
We investigate fundamental localized modes in 2D lattices with an edge (surface). Interaction with the edge expands the stability area for ordinary solitons, and induces a difference between...
Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein Condensates (2006)
Porter, Mason A., Kevrekidis, P. G., Malomed, Boris A., Frantzeskakis, D. J.
We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length $a$ subjected to a spatially periodic modulation, $a=a(x)=a(x+L)$. This...
Mobility of Discrete Solitons in Quadratically Nonlinear Media (2006)
Susanto, H., Kevrekidis, P. G., Carretero-Gonzalez, R., Malomed, Boris A., Frantzeskakis, D. J.
We study the mobility of solitons in second-harmonic-generating lattices. Contrary to what is known for their cubic counterparts, discrete quadratic solitons are mobile not only in the...
Symmetry Breaking in Symmetric and Asymmetric Double-Well Potentials (2006)
Theocharis, G., Kevrekidis, P. G., Frantzeskakis, D. J., Schmelcher, P.
Motivated by recent experimental studies of matter-waves and optical beams in double well potentials, we study the solutions of the nonlinear Schr\"{o}dinger equation in such a context. Using a...
Skyrmion-like excitations in dynamical lattices (2006)
Kevrekidis, P. G., Carretero-Gonzalez, R., Frantzeskakis, D. J., Malomed, B. A., Diakonos, F. K.
We construct discrete analogs of Skyrmions in nonlinear dynamical lattices. The Skyrmion is built as a vortex soliton of a complex field, coupled to a dark radial soliton of a real field. Adjusting...
Dmitriev, S. V., Kevrekidis, P. G., Yoshikawa, N., Frantzeskakis, D. J.
We propose a generalization of the discrete Klein-Gordon models free of the Peierls-Nabarro barrier derived in Nonlinearity {\bf 12}, 1373 (1999) and Phys. Rev. E {\bf 72}, 035602(R) (2005), such...
X,Y,Z-Waves: Extended Structures in Nonlinear Lattices (2006)
Kevrekidis, P. G., Gagnon, J., Frantzeskakis, D. J., Malomed, B. A.
Motivated by recent experimental and theoretical results on optical X-waves, we propose a new type of waveforms in 2D and 3D discrete media -- multi-legged extended nonlinear structures (ENS), built...
Statics and Dynamics of an Inhomogeneously-Nonlinear Lattice (2006)
Machacek, Debra L., Foreman, Elizabeth A., Hoq, Q. E., Kevrekidis, P. G., Saxena, A., Frantzeskakis, D. J., ...
We introduce an inhomogeneously-nonlinear Schr{\"o}dinger lattice, featuring a defocusing segment, a focusing segment and a transitional interface between the two. We illustrate that such...
Polarobreathers in soft potentials (2005)
Cuevas, J., Kevrekidis, P. G., Frantzeskakis, D. J., Bishop, A. R.
We consider polarons in models of coupled electronic and vibrational degrees of freedom, in the presence of a soft nonlinear inter-particle potential (Morse potential). In particular, we focus on a a...
Fractional-Period Excitations in Continuum Periodic Systems (2005)
Nistazakis, H. E., Porter, Mason A., Kevrekidis, P. G., Frantzeskakis, D. J., Nicolin, A., Chin, J. K.
We investigate the generation of fractional-period states in continuum periodic systems. As an example, we consider a Bose-Einstein condensate confined in an optical-lattice potential. We show that...
Theocharis, G., Schmelcher, P., Kevrekidis, P. G., Frantzeskakis, D. J.
We investigate bright matter-wave solitons in the presence of a spatially varying scattering length. It is demonstrated that, even in the absence of any external trapping potential, a soliton can be...
Dynamics and Manipulation of Matter-Wave Solitons in Optical Superlattices (2005)
Porter, Mason A., Kevrekidis, P. G., Carretero-González, R., Frantzeskakis, D. J.
We analyze the existence and stability of bright, dark, and gap matter-wave solitons in optical superlattices. Then, using these properties, we show that (time-dependent) ``dynamical superlattices''...
Discrete Solitons and Vortices on Anisotropic Lattices (2005)
Kevrekidis, P. G., Frantzeskakis, D. J., Carretero-Gonzalez, R., Malomed, B. A., Bishop, A. R.
We consider effects of anisotropy on solitons of various types in two-dimensional nonlinear lattices, using the discrete nonlinear Schr{\"{o}}dinger equation as a paradigm model. For fundamental...
Matter-wave solitons of collisionally inhomogeneous condensates (2005)
Theocharis, G., Schmelcher, P., Kevrekidis, P. G., Frantzeskakis, D. J.
We investigate the dynamics of matter-wave solitons in the presence of a spatially varying atomic scattering length and nonlinearity. The dynamics of bright and dark solitary waves is studied using...
Oscillations of dark solitons in trapped Bose-Einstein condensates (2005)
Pelinovsky, Dmitry E., Frantzeskakis, D. J., Kevrekidis, P. G.
We consider a one-dimensional defocusing Gross--Pitaevskii equation with a parabolic potential. Dark solitons oscillate near the center of the potential trap and their amplitude decays due to...
Stabilizing the Discrete Vortex of Topological Charge S=2 (2005)
Kevrekidis, P. G., Frantzeskakis, D. J.
We study the instability of the discrete vortex with topological charge S=2 in a prototypical lattice model and observe its mediation through the central lattice site. Motivated by this finding, we...
Dynamics of trapped bright solitons in the presence of localized inhomogeneities (2005)
Herring, G., Kevrekidis, P. G., Carretero-Gonzalez, R., Malomed, B. A., Frantzeskakis, D. J., Bishop, A. R.
We examine the dynamics of a bright solitary wave in the presence of a repulsive or attractive localized ``impurity'' in Bose-Einstein condensates (BECs). We study the generation and stability of a...
Carretero-Gonzalez, R., Kevrekidis, P. G., Malomed, B. A., Frantzeskakis, D. J.
We construct a variety of novel localized states with distinct topological structures in the 3D discrete nonlinear Schr{\"{o}}dinger equation. The states can be created in Bose-Einstein condensates...
Vortices in Bose-Einstein Condensates: Some Recent Developments (2005)
Kevrekidis, P. G., Carretero-Gonzalez, R., Frantzeskakis, D. J., Kevrekidis, I. G.
In this brief review we summarize a number of recent developments in the study of vortices in Bose-Einstein condensates, a topic of considerable theoretical and experimental interest in the past few...
Statics, Dynamics and Manipulations of Bright Matter-Wave Solitons in Optical Lattices (2005)
Kevrekidis, P. G., Frantzeskakis, D. J., Carretero-Gonzalez, R., Malomed, B. A., Herring, G., Bishop, A. R.
Motivated by recent experimental achievement in the work with Bose-Einstein condensates (BECs), we consider bright matter-wave solitons, in the presence of a parabolic magnetic trap and a spatially...
Vector solitons with an embedded domain wall (2005)
Kevrekidis, P.G., Susanto, H., Carretero-Gonzalez, R., Malomed, B.A., Frantzeskakis, D.J.
We present a class of soliton solutions to a system of two coupled nonlinear Schrödinger equations, with an intrinsic domain wall (DW) which separates regions occupied by two different fields. The...
Vector solitons with an embedded domain wall (2005)
Kevrekidis, P.G., Susanto, H., Carretero-Gonzalez, R., Malomed, B.A., Frantzeskakis, D.J.
We present a class of soliton solutions to a system of two coupled nonlinear Schrödinger equations, with an intrinsic domain wall (DW) which separates regions occupied by two different fields. The...
Vector solitons with an embedded domain wall (2005)
Kevrekidis, P.G., Susanto, H., Carretero-Gonzalez, R., Malomed, B.A., Frantzeskakis, D.J.
We present a class of soliton solutions to a system of two coupled nonlinear Schrödinger equations, with an intrinsic domain wall (DW) which separates regions occupied by two different fields. The...
Spontaneous Symmetry Breaking in Photonic Lattices: Theory and Experiment (2004)
Kevrekidis, P. G., Chen, Zhigang, Malomed, B. A., Frantzeskakis, D. J., Weinstein, M. I.
We examine an example of spontaneous symmetry breaking in a double-well waveguide with a symmetric potential. The ground state of the system beyond a critical power becomes asymmetric. The effect is...
Nonlinear Schr\"{o}dinger lattices II: Persistence and Stability of Discrete Vortices (2004)
Pelinovsky, D. E., Kevrekidis, P. G., Frantzeskakis, D. J.
We study discrete vortices in the anti-continuum limit of the discrete two-dimensional nonlinear Schr{\"o}dinger (NLS) equations. The discrete vortices in the anti-continuum limit represent a finite...
Nonlinear Schr\"{o}dinger lattices I: Stability of discrete solitons (2004)
Pelinovsky, D. E., Kevrekidis, P. G., Frantzeskakis, D. J.
We consider the discrete solitons bifurcating from the anti-continuum limit of the discrete nonlinear Schr\"{o}dinger (NLS) lattice. The discrete soliton in the anti-continuum limit represents an...
Static and rotating domain-wall crosses in Bose-Einstein condensates (2004)
Malomed, Boris A., Nistazakis, H. E., Frantzeskakis, D. J., Kevrekidis, P. G.
For a Bose-Einstein condensate (BEC) in a two-dimensional (2D) trap, we introduce cross patterns, which are generated by intersection of two domain walls (DWs) separating immiscible species, with...
Deconinck, B., Kevrekidis, P. G., Nistazakis, H. E., Frantzeskakis, D. J.
In this paper, an exact unitary transformation is examined that allows for the construction of solutions of coupled nonlinear Schr{\"o}dinger equations with additional linear field coupling, from...
Rapti, Z., Trombettoni, A., Kevrekidis, P. G., Frantzeskakis, D. J., Malomed, Boris A., Bishop, A. R.
We consider a system of two discrete nonlinear Schr\"{o}dinger equations, coupled by nonlinear and linear terms. For various physically relevant cases, we derive a modulational instability criterion...
Vortices in a Bose-Einstein condensate confined by an optical lattice (2004)
Kevrekidis, P. G., Carretero-González, R., Theocharis, G., Frantzeskakis, D. J., Malomed, B. A.
We investigate the dynamics of vortices in repulsive Bose-Einstein condensates in the presence of an optical lattice (OL) and a parabolic magnetic trap. The dynamics is sensitive to the phase of the...
Stability of dark solitons in a Bose-Einstein condensate trapped in an optical lattice (2004)
Kevrekidis, P. G., Carretero-González, R., Theocharis, G., Frantzeskakis, D. J., Malomed, B. A.
We investigate the stability of dark solitons (DSs) in an effectively one-dimensional Bose-Einstein condensate in the presence of the magnetic parabolic trap and an optical lattice (OL). The analysis...
Three-Dimensional Solitary Waves and Vortices in a Discrete Nonlinear Schr{\"o}dinger Lattice (2004)
Kevrekidis, P. G., Malomed, B. A., Frantzeskakis, D. J., Carretero-González, R.
In a benchmark dynamical-lattice model in three dimensions, the discrete nonlinear Schr{\"{o}}dinger equation, we find discrete vortex solitons with various values of the topological charge $S$....