Publications (551)1064.49 Total impact

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ABSTRACT: We examine conditions for finitetime collapse of the solutions of the defocusing higherorder nonlinear Schr\"odinger (NLS) equation incorporating thirdorder dispersion, selfsteepening, linear and nonlinear gain and loss, and Raman scattering, this is a system that appears in many physical contexts as a more realistic generalization of the integrable NLS. By using energy arguments, it is found that the collapse dynamics is chiefly controlled by the linear/nonlinear gain/loss strengths. We identify a critical value of the linear gain, separating the possible decay of solutions to the trivial zerostate, from collapse. The numerical simulations, performed for a wide class of initial data, are found to be in very good agreement with the analytical results, and reveal longtime stability properties of localized solutions. The role of the higherorder effects to the transient dynamics is also revealed in these simulations. 
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ABSTRACT: We investigate the nonlinear wave dynamics of origamibased metamaterials composed of TachiMiura polyhedron (TMP) unit cells. These cells exhibit strain softening behavior under compression, which can be tuned by modifying their geometrical configurations or initial folded conditions. We assemble these TMP cells into a cluster of origamibased metamaterials, and we theoretically model and numerically analyze their wave transmission mechanism under external impact. Numerical simulations show that origamibased metamaterials can provide a prototypical platform for the formation of nonlinear coherent structures in the form of rarefaction waves, which feature a tensile wavefront upon the application of compression to the system. We also demonstrate the existence of numerically exact traveling rarefaction waves. Origamibased metamaterials can be highly useful for mitigating shock waves, potentially enabling a wide variety of engineering applications. 
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ABSTRACT: In the present work, we explore the possibility of excited breather states in a nonlinear KleinGordon lattice to become nonlinearly unstable, even if they are found to be spectrally stable. The mechanism for this fundamentally nonlinear instability is through the resonance with the wave continuum of a multiple of an internal mode eigenfrequency in the linearization of excited breather states. For the nonlinear instability, the internal mode must have its Krein signature opposite to that of the wave continuum. This mechanism is not only theoretically proposed, but also numerically corroborated through two concrete examples of the KleinGordon lattice with a soft (Morse) and a hard ($\phi^4$) potential. Compared to the case of the nonlinear Schr{\"o}dinger lattice, the Krein signature of the internal mode relative to that of the wave continuum may change depending on the period of the excited breather state. For the periods for which the Krein signatures of the internal mode and the wave continuum coincide, excited breather states are observed to be nonlinearly stable. 
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ABSTRACT: We consider a binary repulsive BoseEinstein condensate in a harmonic trap in one spatial dimension and investigate particular solutions consisting of two darkbright solitons. There are two different stationary solutions characterized by the phase difference in the bright component, inphase and outofphase states. We show that above a critical particle number in the bright component, a symmetrybreaking bifurcation of the pitchfork type occurs that leads to a new asymmetric solution whereas the parental branch, i.e., the outofphase state, becomes unstable. These three different states support different small amplitude oscillations, characterized by an almost stationary density of the dark component and a tunneling of the bright component between the two dark solitons. Within a suitable effective doublewell picture, these can be understood as the characteristic features of a bosonic Josephson junction (BJJ), and we show within a twomode approach that all characteristic features of the BJJ phase space are recovered. For larger deviations from the stationary states, the simplifying doublewell description breaks down due to the feedback of the bright component onto the dark one, causing the solitons to move. In this regime we observe intricate anharmonic and aperiodic dynamics, exhibiting remnants of the BJJ phase space.Physical Review A 04/2015; 91(5):043637. DOI:10.1103/PhysRevA.91.043637 · 2.99 Impact Factor 
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ABSTRACT: We explore a new type of discretizations of lattice dynamical models of the KleinGordon type relevant to the existence and longterm mobility of nonlinear waves. The discretization is based on nonholonomic constraints and is shown to retrieve the "proper" continuum limit of the model. Such discretizations are useful in exactly preserving a discrete analogue of the momentum. It is also shown that for generic initial data, the momentum and energy conservation laws cannot be achieved concurrently. Finally, direct numerical simulations illustrate that our models yield considerably higher mobility of strongly nonlinear solutions than the wellknown "standard" discretizations, even in the case of highly discrete systems when the coupling between the adjacent nodes is weak. Thus, our approach is better suited for cases where an accurate description of mobility for nonlinear traveling waves is important. 
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ABSTRACT: We numerically investigate the influence of interactions on the generalized HongOuMandel (HOM) effect for bosonic particles and show results for the cases of $N=2$, $N=3$ and $N=4$ bosons interacting with a beam splitter, whose role is played by a $\delta$barrier. In particular, we focus on the effect of attractive interactions and compare the results with the repulsive case, as well as with the analytically available results for the noninteracting case (that we use as a benchmark). We observe a fermionization effect both for growing repulsive and attractive interactions, i.e., the dip in the HOM coincidence count is progressively smeared out, for increasing interaction strengths. The role of input asymmetries is also explored.Physics Letters A 03/2015; DOI:10.1016/j.physleta.2015.04.001 · 1.63 Impact Factor 
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ABSTRACT: We introduce a laddershaped chain with each rung carrying a paritytime (PT) symmetric gainloss dimer. The polarity of the dimers is staggered along the chain, meaning alternation of gainloss and lossgain rungs. This structure, which can be implemented as an optical waveguide array, is the simplest one which renders the system PTsymmetric in both horizontal and vertical directions. The system is governed by a pair of linearly coupled discrete nonlinear Schrödinger equations with selffocusing or defocusing cubic onsite nonlinearity. Starting from the analytically tractable anticontinuum limit of uncoupled rungs and using the Newton's method for continuation of the solutions with the increase of the interrung coupling, we construct families of PTsymmetric discrete solitons and identify their stability regions. Waveforms stemming from a single excited rung and double ones are identified. Dynamics of unstable solitons is investigated too.Physical Review E 03/2015; 91(31):033207. · 2.33 Impact Factor 
Article: Transitions from order to disorder in multiple dark and multiple darkbright soliton atomic clouds.
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ABSTRACT: 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 onecomponent, as well as twocomponent, onedimensional atomic gases very close to zero temperature, where in the presence of repulsive interatomic interactions and of a parabolic trap, a cloud of dark (darkbright) solitons can form in the one (two) component system. We corroborate our findings through three distinct types of approaches, namely a GrossPitaevskii type of partial differential equation, particlebased ordinary differential equations describing the soliton dynamical system, and Monte Carlo simulations for the particle system. We define an "empirical" order parameter to characterize the order of the soliton lattices and study how this changes as a function of the strength of the "thermally" (i.e., kinetically) induced perturbations. As may be anticipated by the onedimensional nature of our system, the transition from order to disorder is gradual without, apparently, a genuine phase transition ensuing in the intermediate regime.Physical Review E 03/2015; 91(31):032905. · 2.33 Impact Factor 
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ABSTRACT: The aim of this introductory article is twofold. First, we aim to offer a general introduction to the theme of BoseEinstein condensates, and briefly discuss the evolution of a number of relevant research directions during the last two decades. Second, we introduce and present the articles that appear in this Special Volume of Romanian Reports in Physics celebrating the conclusion of the second decade since the experimental creation of BoseEinstein condensation in ultracold gases of alkalimetal atoms. 
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ABSTRACT: We present a unified description of different types of matterwave solitons that can emerge in quasi onedimensional spinorbit coupled (SOC) BoseEinstein condensates (BECs). This description relies on the reduction of the original twocomponent GrossPitaevskii SOCBEC model to a single nonlinear Schr\"{o}dinger equation, via a multiscale expansion method. This way, we find approximate bright and dark soliton solutions, for attractive and repulsive interatomic interactions respectively, for different regimes of the SOC interactions. Beyond this, our approach also reveals "negative mass" regimes, where corresponding "negative mass" bright or dark solitons can exist for repulsive or attractive interactions, respectively. Such a unique opportunity stems from the structure of the excitation spectrum of the SOCBEC. Numerical results are found to be in excellent agreement with our analytical predictions. 
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ABSTRACT: We study scattering of quasi onedimensional matterwaves 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 wavepacket 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 wavepacket. 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 methods, that treat the soliton as a particle (for moderate and large amplitudes) or a quasilinear wavepacket (for small amplitudes), to determine the critical soliton momentum  as function of the soliton amplitude  for which total reflection is observed. 
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ABSTRACT: In the present work, we consider the mass in mass (or mass with mass) system of granular chains, namely a granular chain involving additionally an internal resonator. For these chains, we rigorously establish that under suitable "antiresonance" conditions connecting the mass of the resonator and the speed of the wave, bellshaped traveling wave solutions continue to exist in the system, in a way reminiscent of the results proven for the standard granular chain of elastic Hertzian contacts. We also numerically touch upon settings where the conditions do not hold, illustrating, in line also with recent experimental work, that nonmonotonic waves bearing nonvanishing tails may exist in the latter case. 
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ABSTRACT: In the present paper we consider an optical system with a $\chi^{(2)}$type nonlinearity and unspecified $\mathcal{PT}$symmetric potential functions. Considering this as an inverse problem and positing a family of exact solutions in terms of cnoidal functions, we solve for the resulting potential functions in a way that ensures the potentials obey the requirements of $\mathcal{PT}$symmetry. We then focus on case examples of soliton and periodic solutions for which we present a stability analysis as a function of their amplitude parameters. Finally, we numerically explore the nonlinear dynamics of the associated waveforms to identify the outcome of the relevant dynamical instabilities of localized and extended states. 
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ABSTRACT: In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as MassinMass systems. We use 3 distinct approaches to identify relevant traveling waves. The first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem. or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) of the problem in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely the avoidance of resonances, that will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric nonvanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of resonance conditions is identified for which solutions with genuinely monotonic decaying tails arise.Journal of Physics A Mathematical and Theoretical 12/2014; 48(19). DOI:10.1088/17518113/48/19/195204 · 1.69 Impact Factor 
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ABSTRACT: In the present paper we consider nonlinear dimers and trimers (more generally, oligomers) embedded within a linear Schr{\"o}dinger lattice where the nonlinear sites are of saturable type. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states. Lastly, we generalize our numerical considerations to the more physically relevant case of Gaussian initial wavepackets and confirm that the asymmetry in the transmission properties also persists in the case of such wavepackets.Photonics 12/2014; 1(4). DOI:10.3390/photonics1040390 
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ABSTRACT: We consider a twodimensional (2D) generalization of a recently proposed model [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 singlesite 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 AC limit, with the same sign across the lattice (they represent the most robust states supported by the lattice, their 1D counterparts being what was considered as 1D bright solitons in the abovementioned work), and the vortex cross, which is specific to the 2D setting. For all the existing states, we explore their stability (analytically, whenever possible). Typical scenarios of instability development are exhibited through direct simulations.Physical Review E 12/2014; 91(4). DOI:10.1103/PhysRevE.91.043201 · 2.33 Impact Factor 
Article: Transitions From Order to Disorder in MultiDark and MultiDarkBright Soliton Atomic Clouds
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ABSTRACT: 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 onecomponent, as well as twocomponent, one dimensional atomic gases very close to zero temperature, where in the presence of repulsive interatomic interactions and of a parabolic trap, a cloud, respectively of dark (darkbright) solitons can form in the one (two) component system. We corroborate our findings through three distinct types of approaches, namely a GrossPitaevskii type of partial differential equation, particlebased ordinary differential equations describing the soliton dynamical system and MonteCarlo simulations for the particle system. We define an "empirical" order parameter to characterize the order of the soliton lattices and study how this changes as a function of the strength of the "thermally" (i.e., kinetically) induced perturbations. As may be anticipated by the onedimensional nature of our system, the transition from order to disorder is gradual without, apparently, a genuine phase transition ensuing in the intermediate regime.Physical Review E 12/2014; 91(3). DOI:10.1103/PhysRevE.91.032905 · 2.33 Impact Factor 
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ABSTRACT: In the present work, we theoretically propose and numerically illustrate a meanfield analogue of the HongOuMandel 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 analogue 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 nearperfect transmission i.e., a $2,0>e$ or a $0,2 >$ state can be constructed instead, very similarly to the quantum mechanical output. We demonstrate this as a generic feature under slight variations of the relative soliton speed, or of the relative amplitude in a wide parametric regime. We also explore how variations of the properties of the "beam splitter" (i.e., the Gaussian barrier) affect this phenomenology.Physical Review A 12/2014; 90(6). DOI:10.1103/PhysRevA.90.063612 · 2.99 Impact Factor 
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ABSTRACT: 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 nonlinearityinduced coupling of the linearization's internal modes of negative energy with the wave continuum. In a broad class of nonlinear Schr{\"o}dinger (NLS) 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 doublewell potential, (b) a twisted localized mode in a onedimensional lattice with cubic nonlinearity, and (c) a discrete vortex in a twodimensional saturable lattice. In all cases, we observe a weak nonlinear instability, despite the linear stability of the respective states. 
Article: Vortex Nucleation in a Dissipative Variant of the Nonlinear Schr\"odinger Equation under Rotation
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ABSTRACT: In the present work, we motivate and explore the dynamics of a dissipative variant of the nonlinear Schr{\"o}dinger equation under the impact of external rotation. As in the well established Hamiltonian case, the rotation gives rise to the formation of vortices. We show, however, that the most unstable mode leading to this instability scales with an appropriate power of the chemical potential $\mu$ of the system, increasing proportionally to $\mu^{2/3}$. The precise form of the relevant formula, obtained through our asymptotic analysis, provides the most unstable mode as a function of the atomic density and the trap strength. We show how these unstable modes typically nucleate a large number of vortices in the periphery of the atomic cloud. However, through a pattern selection mechanism, prompted by symmetrybreaking, only few isolated vortices are pulled in sequentially from the periphery towards the bulk of the cloud resulting in highly symmetric stable vortex configurations with far fewer vortices than the original unstable mode. These results may be of relevance to the experimentally tractable realm of finite temperature atomic condensates.
Publication Stats
8k  Citations  
1,064.49  Total Impact Points  
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 Physical Review E (76)
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Institutions

2001–2015

University of Massachusetts Amherst
 Department of Mathematics and Statistics
Amherst Center, Massachusetts, United States


2014

San Diego State University
 Department of Mathematics and Statistics
San Diego, California, United States


2013

Tel Aviv University
Tell Afif, Tel Aviv, Israel


2011

Universität Heidelberg
 KirchhoffInstitute of Physics
Heidelburg, BadenWürttemberg, Germany


2001–2011

Princeton University
 • Department of Mathematics
 • Department of Chemical and Biological Engineering
 • Program in Applied and Computational Mathematics
Princeton, New Jersey, United States


2007

University of Crete
Retimo, Crete, Greece 
University of Kansas
 Department of Mathematics
Lawrence, Kansas, United States


2006

Nankai University
T’ienchingshih, Tianjin Shi, China


2005

University of New Mexico
 Department of Mathematics & Statistics
Albuquerque, New Mexico, United States


2004

The University of Tokyo
 Institute of Industrial Science
Tokyo, Tokyoto, Japan


2000–2003

Los Alamos National Laboratory
 • Center for Nonlinear Studies
 • Theoretical Division
ЛосАламос, California, United States


1999–2001

Rutgers, The State University of New Jersey
 Department Physics and Astronomy
Newark, NJ, United States
