arXiv subjects

P. G. Kevrekidis

Publications and source records attributed to P. G. Kevrekidis.

At least 109 records · Page 6Linked to original sources

arXiv2021

Transverse instability and dynamics of nonlocal bright solitons

We study the transverse instability and dynamics of bright soliton stripes in two-dimensional nonlocal nonlinear media. Using a multiscale perturbation method, we derive analytically the first-order correction to the soliton shape, which features an exponential growth in time -- a signature of the transverse instability. The soliton's characteristic timescale associated with its exponential growth,is found to depend on the square root of the nonlocality parameter. This, in turn, highlights the nonlocality-induced suppression of the transverse instability. Our analytical predictions are corroborated by direct numerical simulations, with the analytical results being in good agreement with the numerical ones.

nlin.PS↗

arXiv2021

Pairwise Interactions of Ring Dark Solitons with Vortices and other Rings: Stationary States, Stability Features and Nonlinear Dynamics

In the present work, we explore analytically and numerically the co-existence and interactions of ring dark solitons (RDSs) with other RDSs, as well as with vortices. The azimuthal instabilities of the rings are explored via the so-called filament method. As a result of their nonlinear interaction, the vortices are found to play a stabilizing role on the rings, yet their effect is not sufficient to offer complete stabilization of RDSs. Nevertheless, complete stabilization of the relevant configuration can be achieved by the presence of external ring-shaped barrier potentials. Interactions of multiple rings are also explored, and their equilibrium positions (as a result of their own curvature and their tail-tail interactions) are identified. In this case too, stabilization is achieved via multi-ring external barrier potentials.

nlin.PS↗

arXiv2021

Solitons and soliton interactions in repulsive spinor Bose-Einstein condensates with non-zero background

We characterize the soliton solutions and their interactions for a system of coupled evolution equations of nonlinear Schrödinger (NLS) type that models the dynamics in one-dimensional repulsive Bose-Einstein condensates with spin one, taking advantage of the representation of such model as a special reduction of a 2 x 2 matrix NLS system. Specifically, we study in detail the case in which solutions tend to a non-zero background at space infinities. First we derive a compact representation for the multi-soliton solutions in the system using the Inverse Scattering Transform (IST). We introduce the notion of canonical form of a solution, corresponding to the case when the background is proportional to the identity. We show that solutions for which the asymptotic behavior at infinity is not proportional to the identity, referred to as being in non-canonical form, can be reduced to canonical form by unitary transformations that preserve the symmetric nature of the solution (physically corresponding to complex rotations of the quantization axes). Then we give a complete characterization of the two families of one-soliton solutions arising in this problem, corresponding to ferromagnetic and to polar states of the system, and we discuss how the physical parameters of the solitons for each family are related to the spectral data in the IST. We also show that any ferromagnetic one-soliton solution in canonical form can be reduced to a single dark soliton of the scalar NLS equation, and any polar one-soliton solution in canonical form is unitarily equivalent to a pair of oppositely polarized displaced scalar dark solitons up to a rotation of the quantization axes. Finally, we discuss two-soliton interactions and we present a complete classification of the possible scenarios that can arise depending on whether either soliton is of ferromagnetic or polar type.

cond-mat.quant-gas↗

arXiv2021

Localization in optical systems with an intensity-dependent dispersion

We address the nonlinear Schrodinger equation with intensity-dependent dispersion which was recently proposed in the context of nonlinear optical systems. Contrary to the previous findings, we prove that no solitary wave solutions exist if the sign of the intensity-dependent dispersion coincides with the sign of the constant dispersion, whereas a continuous family of such solutions exists in the case of the opposite signs. The family includes two particular solutions, namely cusped and bell-shaped solitons, where the former represents the lowest energy state in the family and the latter is a limit of solitary waves in a regularized system. We further analyze the delicate analytical properties of these solitary waves such as the asymptotic behavior near singularities, the spectral stability, and the convergence of the fixed-point iterations near such solutions. The analytical theory is corroborated by means of numerical approximations.

nlin.PS↗

arXiv2021

Kink-Antikink Collisions and Multi-Bounce Resonance Windows in Higher-Order Field Theories

We study collisions of coherent structures in higher-order field-theoretic models, such as the $ϕ^8$, $ϕ^{10}$ and $ϕ^{12}$ ones. The main distinguishing feature, of the example models considered herein, is that the collision arises due to the long-range interacting algebraic tails of these solitary waves. We extend the approach to suitably initialize the relevant kinks, in the additional presence of finite initial speed, in order to minimize the dispersive wave radiation potentially created by their slow spatial decay. We find that, when suitably initialized, these models still feature the multi-bounce resonance windows earlier found in models in which the kinks bear exponential tails, such as the $ϕ^4$ and $ϕ^6$ field theories among others. Also present is the self-similar structure of the associated windows with three- and more-bounce windows at the edges of two- and lower-bounce ones. Moreover, phenomenological, but highly accurate (and predictive) scaling relations are derived for the dependence of the time between consecutive collisions and, e.g., the difference in kinetic energy between the incoming one and the critical one for one-bounces. Such scalings are traced extensively over two-bounce collision windows throughout the three models, hinting at the possibility of an analytical theory in this direction.

hep-th↗

arXiv2021

Onset and Irreversibility of Granulation of Bose-Einstein condensates under Feshbach Resonance Management

Granulation of quantum matter -- the formation of persistent small-scale patterns -- is realized in the images of quasi-one-dimensional Bose-Einstein condensates perturbed by a periodically modulated interaction. Our present analysis of a mean-field approximation suggests that granulation is caused by the gradual transformation of phase undulations into density undulations. This is achieved by a suitably large modulation frequency, while for low enough frequencies the system exhibits a quasi-adiabatic regime. We show that the persistence of granulation is a result of the irregular evolution of the phase of the wavefunction representing an irreversible process. Our model predictions agree with numerical solutions of the Schrödinger equation and experimental observations. The numerical computations reveal the emergent many-body correlations behind these phenomena via the multi-configurational time-dependent Hartree theory for bosons (MCTDHB).

cond-mat.quant-gas↗

arXiv2021

Unstable dynamics of solitary traveling waves in a lattice with long-range interactions

In this work we revisit the existence, stability and dynamics of unstable traveling solitary waves in the context of lattice dynamical systems. We consider a nonlinear lattice of an $α$-Fermi-Pasta-Ulam type with the additional feature of all-to-all harmonic long-range interactions whose strength decays exponentially with distance. The competition between the nonlinear nearest-neighbor terms and the longer-range linear ones yields two parameter regimes where the dependence of the energy $H$ of the traveling waves on their velocity $c$ is non-monotonic and multivalued, respectively. We examine both cases, and identify the exact (up to a prescribed numerical tolerance) traveling waves. To investigate the stability of the obtained solutions, we compute their Floquet multipliers, thinking of the traveling wave problem as a periodic one modulo shifts. We show that in the general case when the relationship between $H$ and $c$ is not single-valued, the sufficient but not necessary criterion for stability change is $H'(s)=0$, where $s$ is the parameter along the energy-velocity curve. Perturbing the unstable solutions along the corresponding eigenvectors, we identify two different scenarios of the dynamics of their transition to stable branches. In the first one, the perturbed wave slows down after expelling a dispersive wave. The second scenario involves an increase in the velocity of the perturbed wave accompanied by the formation of a slower small-amplitude traveling solitary wave.

nlin.PS↗

arXiv2021

Dynamics of two languages competing on a network: a case study

A language dynamics model on a square lattice, which is an extension of the one popularized by Abrams and Strogatz [1], is analyzed using ODE bifurcation theory. For this model we are interested in the existence and spectral stability of structures such as stripes, which are realized through pulses and/or the concatenation of fronts, and spots, which are a contiguous collection of sites in which one language is dominant. Because the coupling between sites is nonlinear, the boundary between sites containing speaking two different languages is "sharp"; in particular, in a PDE approximation it allows for the existence of compactly supported pulses (compactons). The dynamics are considered as a function of the prestige of a language. In particular, it is seen that as the prestige varies, it allows for a language to spread through the network, or conversely for its demise.

nlin.PS↗

arXiv2021

Phase Diagram, Stability and Magnetic Properties of Nonlinear Excitations in Spinor Bose-Einstein Condensates

We present the phase diagram, the underlying stability and magnetic properties as well as the dynamics of nonlinear solitary wave excitations arising in the distinct phases of a harmonically confined spinor $F=1$ Bose-Einstein condensate. Particularly, it is found that nonlinear excitations in the form of dark-dark-bright solitons exist in the antiferromagnetic and in the easy-axis phase of a spinor gas, being generally unstable in the former while possessing stability intervals in the latter phase. Dark-bright-bright solitons can be realized in the polar and the easy-plane phases as unstable and stable configurations respectively; the latter phase can also feature stable dark-dark-dark solitons. Importantly, the persistence of these types of states upon transitioning, by means of tuning the quadratic Zeeman coefficient from one phase to the other is unravelled. Additionally, the spin-mixing dynamics of stable and unstable matter waves is analyzed, revealing among others the coherent evolution of magnetic dark-bright, nematic dark-bright-bright and dark-dark-dark solitons. Moreover, for the unstable cases unmagnetized or magnetic droplet-like configurations and spin-waves consisting of regular and magnetic solitons are seen to dynamically emerge remaining thereafter robust while propagating for extremely large evolution times. Interestingly, exposing spinorial solitons to finite temperatures, their anti-damping in trap oscillation is showcased. It is found that the latter is suppressed for stronger bright soliton component "fillings". Our investigations pave the wave for a systematic production and analysis involving spin transfer processes of such waveforms which have been recently realized in ultracold experiments.

nlin.PS↗

arXiv2020

Kink-Antikink Interaction Forces and Bound States in a $ϕ^4$ Model with Quadratic and Quartic dispersion

We consider the interaction of solitary waves in a model involving the well-known $ϕ^4$ Klein-Gordon theory, but now bearing both Laplacian and biharmonic terms with different prefactors. As a result of the competition of the respective linear operators, we obtain three distinct cases as we vary the model parameters. In the first the biharmonic effect dominates, yielding an oscillatory inter-wave interaction; in the third the harmonic effect prevails yielding exponential interactions, while we find an intriguing linearly modulated exponential effect in the critical second case, separating the above two regimes. For each case, we calculate the force between the kink and antikink when initially separated with sufficient distance. Being able to write the acceleration as a function of the separation distance, and its corresponding ordinary differential equation, we test the corresponding predictions, finding very good agreement, where appropriate, with the corresponding partial differential equation results. Where the two findings differ, we explain the source of disparities. Finally, we offer a first glimpse of the interplay of harmonic and biharmonic effects on the results of kink-antikink collisions and the corresponding single- and multi-bounce windows.

nlin.PS↗

arXiv2020

Thermalization in the one-dimensional Salerno model lattice

The Salerno model constitutes an intriguing interpolation between the integrable Ablowitz-Ladik (AL) model and the more standard (non-integrable) discrete nonlinear Schr{ö}dinger (DNLS) one. The competition of local on-site nonlinearity and nonlinear dispersion governs the thermalization of this model. Here, we investigate the statistical mechanics of the Salerno one-dimensional lattice model in the nonintegrable case and illustrate the thermalization in the Gibbs regime. As the parameter interpolating between the two limits (from DNLS towards AL) is varied, the region in the space of initial energy and norm-densities leading to thermalization expands. The thermalization in the non-Gibbs regime heavily depends on the finite system size; we explore this feature via direct numerical computations for different parametric regimes.

physics.class-ph↗

arXiv2020

Dark-Antidark Spinor Solitons in Spin-1 Bose Gases

We consider a one-dimensional trapped spin-1 Bose gas and numerically explore families of its solitonic solutions, namely antidark-dark-antidark (ADDAD), as well as dark-antidark-dark (DADD) solitary waves. Their existence and stability properties are systematically investigated within the experimentally accessible easy-plane ferromagnetic phase by means of a continuation over the atom number as well as the quadratic Zeeman energy. It is found that ADDADs are substantially more dynamically robust than DADDs. The latter are typically unstable within the examined parameter range. The dynamical evolution of both of these states is explored and the implication of their potential unstable evolution is studied. Some of the relevant observed possibilities involve, e.g., symmetry-breaking instability manifestations for the ADDAD, as well as splitting of the DADD into a right- and a left-moving dark-antidark pair with the anti-darks residing in a different component as compared to prior to the splitting. In the latter case, the structures are seen to disperse upon long-time propagation.

cond-mat.quant-gas↗

arXiv2020

Universal reductions and solitary waves of weakly nonlocal defocusing nonlinear Schrödinger equations

We study asymptotic reductions and solitary waves of a weakly nonlocal defocusing nonlinear Schrödinger (NLS) model. The hydrodynamic form of the latter is analyzed by means of multiscale expansion methods. To the leading-order of approximation (where only the first moment of the response function is present), we show that solitary waves, in the form of dark solitons, are governed by an effective Boussinesq/Benney- Luke (BBL) equation, which describes bidirectional waves in shallow water. Then, for long times, we reduce the BBL equation to a pair of Korteweg-de Vries (KdV) equations for right- and left-going waves, and show that the BBL solitary wave transforms into a KdV soliton. In addition, to the next order of approximation (where both the first and second moment of the response function are present), we find that dark solitons are governed by a higher-order perturbed KdV (pKdV) equation, which has been used to describe ion-acoustic solitons in plasmas and water waves in the presence of higherorder effects. The pKdV equation is approximated by a higher-order integrable system and, as a result, only insubstantial changes in the soliton shape and velocity are found, while no radiation tails (in this effective KdV picture) are produced.

nlin.PS↗

arXiv2020

Breather stripes and radial breathers of the two-dimensional sine-Gordon equation

We revisit the problem of transverse instability of a 2D breather stripe of the sine-Gordon (sG) equation. A numerically computed Floquet spectrum of the stripe is compared to analytical predictions developed by means of multiple-scale perturbation theory showing good agreement in the long-wavelength limit. By means of direct simulations, it is found that the instability leads to a breakup of the quasi-1D breather in a chain of interacting 2D radial breathers that appear to be fairly robust in the dynamics. The stability and dynamics of radial breathers in a finite domain are studied in detail by means of numerical methods. Different families of such solutions are identified. They develop small-amplitude spatially oscillating tails ("nanoptera") through a resonance of higher-order breather's harmonics with linear modes ("phonons") belonging to the continuous spectrum. These results demonstrate the ability of the 2D sG model within our finite domain computations to localize energy in long-lived, self-trapped breathing excitations.

nlin.PS↗

arXiv2020

Deflation-based Identification of Nonlinear Excitations of the 3D Gross--Pitaevskii equation

We present previously unknown solutions to the 3D Gross--Pitaevskii equation describing atomic Bose-Einstein condensates. This model supports elaborate patterns, including excited states bearing vorticity. The discovered coherent structures exhibit striking topological features, involving combinations of vortex rings and multiple, possibly bent vortex lines. Although unstable, many of them persist for long times in dynamical simulations. These solutions were identified by a state-of-the-art numerical technique called deflation, which is expected to be applicable to many problems from other areas of physics.

nlin.PS↗

arXiv2020

Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices

We conduct an extensive study of nonlinear localized modes (NLMs), which are temporally periodic and spatially localized structures, in a two-dimensional array of repelling magnets. In our experiments, we arrange a lattice in a hexagonal configuration with a light-mass defect, and we harmonically drive the center of the chain with a tunable excitation frequency, amplitude, and angle. We use a damped, driven variant of a vector Fermi- Pasta-Ulam-Tsingou lattice to model our experimental setup. Despite the idealized nature of the model, we obtain good qualitative agreement between theory and experiments for a variety of dynamical behaviors. We find that the spatial decay is direction-dependent and that drive amplitudes along fundamental displacement axes lead to nonlinear resonant peaks in frequency continuations that are similar to those that occur in one-dimensional damped, driven lattices. However, driving along other directions leads to the creation of asymmetric NLMs that bifurcate from the main solution branch, which consists of symmetric NLMs. When we vary the drive amplitude, we observe such behavior both in our experiments and in our simulations. We also demonstrate that solutions that appear to be time-quasi-periodic bifurcate from the branch of symmetric time-periodic NLMs.

nlin.PS↗

arXiv2020

On-demand generation of dark soliton trains in Bose-Einstein condensates

Matter-wave interference mechanisms in one-dimensional Bose-Einstein condensates that allow for the controlled generation of dark soliton trains upon choosing suitable box-type initial configurations are described. First, the direct scattering problem for the defocusing nonlinear Schrödinger equation with nonzero boundary conditions and general box-type initial configurations is discussed, and expressions for the discrete spectrum corresponding to the dark soliton excitations generated by the dynamics are obtained. It is found that the size of the initial box directly affects the number, size and velocity of the solitons, while the initial phase determines the parity of the solutions. The analytical results are compared to those of numerical simulations of the Gross-Pitaevskii equation, both in the absence and in the presence of a harmonic trap. The numerical results bear out the analytical results with excellent agreement.

cond-mat.quant-gas↗

arXiv2020

Propagation of periodic wave trains along the magnetic field in a collision-free plasma

In this work, a systematic study, examining the propagation of periodic and solitary wave along the magnetic field in a cold collision-free plasma, is presented. Employing the quasi-neutral approximation and the conservation of momentum flux and energy flux in the frame co-traveling with the wave, the exact analytical solution of the stationary solitary pulse is found analytically in terms of particle densities, parallel and transverse velocities, as well as transverse magnetic fields. Subsequently, this solution is generalized in the form of periodic waveforms represented by cnoidal-type waves. These considerations are fully analytical in the case where the total angular momentum flux $L$, due to the ion and electron motion together with the contribution due to the Maxwell stresses, vanishes. A graphical representation of all associated fields is also provided.

nlin.PS↗