arXiv subjects

P. G. Kevrekidis

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

At least 19 recordsLinked to original sources

arXiv2026

Radial dam breaks in a two-dimensional droplet bearing environment

The controlled dynamical generation of radial dam break flows (DBFs) is demonstrated in two-dimensional droplet environments. These ultracold mixtures feature competing mean-field and quantum fluctuation effects and are initialized on a disk-shaped uniform density. Depending on the value of the latter, reflecting also the dominance of attractive or repulsive interactions, three dynamical response regimes are identified. At small densities a moving wavetrain of bright ring solitons is observed (dubbed ring DBF), at intermediate densities a ring kink-dispersive shock wave, while at large densities the flows encompass composite ring kink-rarefaction waves moving towards the center. The emergence of these patterns, whose formation would be prohibited in two-dimensional Kerr media due to wave-collapse, is rooted in the competition between attraction and repulsion inherent to droplet environments, modeled by the extended Gross-Pitaevskii equation. The characterization of the ensuing nonlinear waveforms is further corroborated by reduced models based on the cubic-quintic nonlinear Schrödinger equation. The different wave patterns emanating from dam break flows can be experimentally realized using current state-of-the-art ultracold atom experiments.

cond-mat.quant-gas↗

arXiv2026

Optical creation of dark-bright soliton lattices in one-dimensional multicomponent Bose-Einstein condensates

We present a widely accessible and experimentally realizable technique for the controlled creation of dark-bright solitons and soliton lattices in one-dimensional atomic Bose-Einstein condensates. The method is based on preparing the condensate in a dark state of a $Λ$-coupled three-level system. Numerical simulations of the corresponding two-component system reveal that individual dark-bright solitons created through this scheme can survive over experimentally accessible timescales, even when the coupling laser fields are switched off. Meanwhile, the fate of soliton lattices upon the quench of the fields depends on the scattering lengths. When they are all equal, the lattice is found to persist on timescales comparable to the condensate lifetime, even though the analysis of dynamical stability reveals that they possess unstable modes. In this case the resulting destabilization is not found to be detrimental, as it leads to recurrent dynamics. However, for unequal scattering lengths the lattice structure gets destroyed once the instability sets in, which happens after a few tens of milliseconds after the quench of the optical fields.

cond-mat.quant-gas↗

arXiv2026

Blowup of Multi-Peaked Waveforms in the Two-Dimensional Nonlinear Schroedinger Model

In the present work, we explore the self-focusing and resulting collapse of two-dimensional waveforms involving multiple pulses in a nonlinear Schroedinger equation with a general power-law nonlinearity. We find that a wide range of multi-peaked states bifurcate from the critical threshold of the cubic nonlinearity, thus representing ``bifurcations from infinity'', i.e., the relevant pulses start at infinite distance in the critical limit and draw nearer, as the nonlinearity exponent increases past that threshold. We identify the resulting ``interacting particle system'' as amounting to a force balance between the exponentially interacting tails (modulated by a suitable power law) and a linear phase-induced force. The equilibria emerging from this force balance are found to be in excellent agreement with the identified steady states of the partial differential equation. The spectral stability of multi-peaked configurations is analyzed, leading to the conclusion that all the relevant states are less stable than the single-peak collapsing solution whose stability was analyzed earlier. Indeed, we reveal both symmetry-breaking, as well as motion-inducing destabilizing dynamics, with the former ones among them being dominant and ultimately leading to a single dominant collapse spot. Moreover, we characterize systematically both the real and imaginary eigenvalues of multi-peaked configurations, partitioning them in groups of different sizes, described by powers of the solution's blowup rate G.

nlin.PS↗

arXiv2026

Two-dimensional solitons in extended GPE models with Lee-Huang-Yang corrections

We investigate the existence and dynamics of two-dimensional solitary waves in a quantum droplet environment described by the extended Gross-Pitaevskii equation featuring logarithmic mean-field and Lee-Huang-Yang interactions. In the modulationally stable regime of the background, we employ suitable multiscale asymptotic methods to derive effective nonlinear integrable models corresponding to the Kadomtsev-Petviashvili and Davey-Stewartson equations. Based on these reduced models, we construct approximate analytical solutions describing line solitons, algebraically localized lump solitons, ring solitons, and exponentially localized dromions embedded on the droplet background. The dynamical robustness of these solutions is monitored through numerical simulations. Line, lump and ring solitons stay closest to the theoretical predictions, although progressively deviate due to the emergence of small-amplitude radiation, while dromions depart from their analytical waveform the most, although they roughly maintain their shape. Our results unveil unprecedented multidimensional soliton solutions in models featuring the competition of mean-field and quantum fluctuations and as such are amenable to current ultracold atom experiments.

cond-mat.quant-gas↗

arXiv2026

Correlated many-body quantum dynamics of the Peregrine soliton

We explore the correlated dynamics underlying the formation of the quantum Peregrine soliton, a prototypical rogue-wave excitation, utilizing interaction quenches from repulsive to attractive couplings in an ultracold bosonic gas confined in a one-dimensional box trap. The latter emulates the so-called semi-classical initial conditions and the associated gradient catastrophe scenario facilitating the emergence of a high-density, doubly localized waveform. The ensuing multi-orbital variant of the Peregrine soliton features notable deviations from its mean-field sibling, including a reduced peak amplitude, wider core, absence of the side density dips, and earlier formation times. Moreover, Peregrine soliton generation yields coherence losses, while experiencing two-body bunching within each of its sides which show anti-bunching between each other. Controllable seeding of the Peregrine soliton is also demonstrated by tuning the atom number or the box length, while reducing the latter favors the generation of the time-periodic Kuznetsov-Ma breather. Our results highlight that correlations reshape the morphology of rogue-waves in the genuinely quantum, nonintegrable realm, while setting the stage for the emergent field of quantum dispersive hydrodynamics.

cond-mat.quant-gas↗

arXiv2026

Optical Thermodynamics Beyond the Weak Nonlinearity Limit

Optical thermodynamics has recently emerged as a theoretical framework describing a Rayleigh-Jeans (RJ) modal power distribution of multimoded nonlinear photonic circuits. However, its applicability is constrained to systems exhibiting weak nonlinear mode-mode interactions. Here, by employing a Transfer Integral Operator, we circumvent this limitation and establish a steady-state interacting RJ modal distribution -- referred to as non-ideal RJ (NIRJ) -- with renormalized temperature and optical chemical potential. This also builds a natural bridge with earlier work on grand-canonical statistical-mechanical formulations of discrete nonlinear systems. The theory derives the optical analogue of the compressibility factor, which controls the transition from an ideal, non-interacting equation of state (EoS) to a van der Waals-like interacting EoS.

nlin.PS↗

arXiv2026

Spin mixing induced dynamics of spinor solitons in $F=1$ Bose Einstein condensates

We explore soliton interactions in a homogeneous spinor $F=1$ Bose Einstein Condensate (BEC) in the presence of a magnetic field, focusing on dark bright dark and bright dark bright configurations. We investigate how these interactions depend on the phase differences among bright solitons and their influence during the dynamics. Our findings align with prior non spinor results, i.e., repulsion among in phase bright solitons and attraction among out of phase pairs in self repulsive atomic BECs. The potential bright soliton attraction, added to the short range repulsion of dark dark soliton interactions, can lead to bound states. However, we find that these bound states break in the presence of spinor interactions due to the particle exchange dynamics between the hyperfine states of the components. Additonally, we develop an effective classical model to describe the soliton dynamics, using a Lagrangian approach. The accuracy of the model is tested by comparing it against numerical simulations. Our results suggest that the proposed model captures the essential features of soliton behavior in the presence of spin interactions, and provides congruent soliton trajectories and interspecies particle exchange dynamics in most of the cases.

cond-mat.quant-gas↗

arXiv2026

Solitary waves and vortices in a Nonlinear Schrödinger equation with ponderomotive nonlinearity

In the present work we revisit a ponderomotive nonlinearity model used to examine self-trapped laser beams in plasma. Upon briefly considering the exact stationary 1D solutions of the model, we extend considerations to two spatial dimensions where we find both solitonic and vortical structures. The solitary waves localized in both directions are found to be spectrally stable. However, all other structures that we consider in this model, including line solitons -- which are homogeneous 2D extensions of 1D solitons -- and vortices of topological charge S=1 and S=2 are found to be spectrally unstable. The focal point of our studies then turns to the examination of the collisions of the stable two-dimensional solitary waves for which we map a two-parameter space of soliton speeds and frequencies, in terms of the potential outcomes. While the standard scenarios of merger, inelastic collision leading to separation, separation that leaves behind a localized pulse are all possible, the intriguing outcome that we highlight here is that of a longitudinal collision yielding a transverse spliting of the solitons, either with or without a localized pulse remnant.

nlin.PS↗

arXiv2026

Exponential Asymptotics for Dark Solitons of the Discrete NLS Model

In the present work we revisit the problem of the dark solitary wave pinned in the discrete nonlinear Schr{ö}dinger equation. In a number of recent studies, the methodology of exponential asymptotics was attempted to be utilized in this problem, however the results were not found to be fully in agreement with associated multiprecision numerical computations. Here we resolve this conundrum by finding precise exponential asymptotics for the pinned dark solitary waves. Moreover, we reconcile the relevant result with a general theory of pinned dark solitary waves in the {\it continuum} nonlinear Schr{ö}dinger equations in the presence of external potentials.

nlin.PS↗

arXiv2026

Extreme (Rogue) Waves: From Theory to Experiments in Ultracold Gases and Beyond

In this Chapter, we review key theoretical and experimental advances in the study of extreme nonlinear wave events, called rogue waves (RWs), in both single-component attractively interacting and two-component repulsive mixtures of ultracold quantum gases. Starting from the exact rational solutions of the integrable focusing nonlinear Schroedinger model, the hierarchy of RW solutions is exemplified. These range from the Peregrine soliton (PS) and, related to it, the destabilization into a multi-peak cascade of PSs dubbed "Christmas-tree", to the Akhmediev breather, and Kuznetsov-Ma soliton as well as higher-order RWs. Emphasis is placed on their controllable dynamical emergence and characteristics in non-integrable quantum many-body systems described by Gross-Pitaevskii models and extensions thereof through different protocols such as modulational instability, gradient catastrophe, and dam-break flows. We further discuss how immiscible particle-imbalanced repulsive mixtures can be cast into effective attractive single-component environments capable of hosting RWs. Next, state-of-the-art experimental techniques are summarized within the ultracold realm that can be utilized to realize solitary waves, modulational instability, dispersive shock waves and RWs including the very recent first experimental observation of the PS, enabled through engineered effective focusing interactions and precise dynamical triggering. Observations of these extreme events in water waves, nonlinear optics and beyond are also outlined, highlighting their broader relevance and potential of emergence in disparate physical settings. Our exposition aims at showcasing ultracold atomic gases as versatile platforms for controllably generating and probing extreme nonlinear events, among others, in the quantum realm across integrable and non-integrable settings.

cond-mat.quant-gas↗

arXiv2026

Bright Fractional Single and Multi-Solitons in a Prototypical Nonlinear Schr{ö}dinger Paradigm: Existence, Stability and Dynamics

In the present work we explore features of single and pairs of solitary waves in a fractional variant of the nonlinear Schr{ö}dinger equation. Motivated by the recent experimental realization of arbitrary fractional exponents, upon quantifying the tail properties of such coherent structures, we detail their destabilization when the fractional exponent $α$ acquires values $α<1$ and showcase how the relevant destabilization is associated with collapse type phenomena. We then turn to in- and out-of-phase pairs of such waveforms and illustrate how they generically exist for arbitrary $α$ when we cross the harmonic limit, i.e., for $α>2$. Importantly, we use the parameter $α$ as a ``bifurcation parameter'' in order to connect the harmonic ($α=2$) and biharmonic ($α=4$) limits. Remarkably, not only do we retrieve the instability of all solitonic pairs in the biharmonic case, but showcase a stabilization feature of particular branches of such multipulses that is {\it unique} to the fractional case and does not arise -- to our knowledge -- for integer multi-pulse settings. We explain systematically this stabilization via spectral analysis and expand upon the implications of our results for the potential observability of fractional multipulse solitary waves.

nlin.PS↗

arXiv2025

Pattern formation in ring condensates subjected to bichromatic driving

We investigate the dynamical formation of nonlinear patterns in one-dimensional ring condensates under bichromatic periodic modulation of the interaction strength. The stability phase diagram of the condensate's homogeneous density state is analytically derived through a suitable biharmonic variant of the Mathieu equation and computing the associated Floquet spectrum. It reveals the complex interplay between the driving parameters, i.e., amplitude, frequencies, and the so-called frequencies' mixing angle, which dictate the instability onset and the selective enhancement of higher-order resonance tongues, thus offering precise control over the excited modes. These results are in agreement with time-dependent mean-field simulations evidencing the emergence of density wave modulations of specific momenta, while enabling a deeper understanding of the nonlinear stage of the relevant instability. Further insights on the ensuing unstable nonlinear dynamics are provided through a reduced {five-mode} model which captures the instability onset, the oscillatory behavior of the mode populations and the phase-space dynamics, in agreement with the mean-field predictions. Our study highlights the versatility of bichromatic driving to generate and control complex nonlinear patterns that are within reach in present day ultracold atom experiments.

cond-mat.quant-gas↗

arXiv2025

Observation of vector rogue waves in repulsive three-component atomic mixtures

We report the experimental observation of vector extensions of Peregrine solitons in highly particle-imbalanced, pairwise immiscible three-component repulsive Bose-Einstein condensates (BECs). The possibility of an effectively attractive character of the minority components is established by constructing a generalized reduction scheme for an imbalanced N-component setup with arbitrary interaction signs. These components may suffer intra- and inter-component modulation instability, which along with the presence of an attractive potential well induces the dynamical formation of highly reproducible vector rogue waves. Exploiting different Rb hyperfine states, it is possible to flexibly tune the effective interactions stimulating the realization of a plethora of vector rogue waves, including single and double Peregrine-like wave peaks. The experimental findings are in quantitative agreement with suitable three-dimensional mean-field simulations, while quasi-one-dimensional analysis of the non-polynomial Schrödinger model provides additional insights into the rogue wave characteristics.

cond-mat.quant-gas↗

arXiv2025

Nonlinear stage of modulational instability in repulsive two-component Bose-Einstein condensates

Modulational instability (MI) is a fundamental phenomenon in the study of nonlinear dynamics, spanning diverse areas such as shallow water waves, optics, and ultracold atomic gases. In particular, the nonlinear stage of MI has recently been a topic of intense exploration, and has been shown to manifest, in many cases, in the generation of dispersive shock waves (DSWs). In this work, we experimentally probe the MI dynamics in an immiscible two-component ultracold atomic gas with exclusively repulsive interactions, catalyzed by a hard-wall-like boundary produced by a repulsive optical barrier. We analytically describe the expansion rate of the DSWs in this system, generalized to arbitrary inter-component interaction strengths and species ratios. We observe excellent agreement among the analytical results, an effective 1D numerical model, full 3D numerical simulations, and experimental data. Additionally, we extend this scenario to the interaction between two counterpropagating DSWs, which leads to the production of Peregrine soliton structures. These results further demonstrate the versatility of atomic platforms towards the controlled realization of DSWs and rogue waves.

cond-mat.quant-gas↗

arXiv2025

The vortex comb: eliminating vortices from Bose-Einstein condensates using optical lattices

In the present work we introduce and explore a technique for the efficient removal of vortices from an atomic Bose-Einstein condensate, through the application and subsequent removal of a one-dimensional optical lattice. We showcase a prototypical experimental realization of the technique that motivates a detailed theoretical study of vortex removal mechanisms. Through simulations of the condensate dynamics during application of the optical lattice, we also discover a vortex removal mechanism that arises in narrow, optical-lattice-induced atomic density channels for which the channel width is on the order of the nominal vortex core size and healing length. This mechanism involves the density profile typically associated with a vortex core spatially separating from the phase singularity associated with the vortex. By analyzing numerical experiments covering a wide range of variations of the optical lattice amplitude and fringe periodicity, we identify the existence of an optimal set of parameters that enables the efficient removal of all vortices from the condensate. This analysis paves the way for further studies aimed at understanding vortex dynamics in narrow channels, and adds to an experimental toolkit for working with vortices and controlling the dynamical states of condensates.

cond-mat.quant-gas↗

arXiv2025

Realization and characterization of an all-bands-flat electrical lattice

We construct an electrical all-bands-flat (ABF) lattice and experimentally generate compact localized states (CLSs) therein. The lattice is a diamond (rhombic) chain and implemented as a network of capacitors and inductors, as well as voltage inverters (using operational amplifiers) in order to introduce a $π$-phase flux within each diamond. The network's normal modes split into three flat bands, and the corresponding CLSs can be excited in isolation via a two-node driving at the flat band frequencies. We also examine the role of the lattice edges and their interaction with the CLSs. Finally, we compare the experimental results to tight-binding predictions and obtain very good agreement. This analysis paves the way for further experimental implementations of ABF systems in electric networks, especially with an eye towards exploring their interplay with nonlinearity.

cond-mat.mes-hall↗

arXiv2025

On a Klein-Gordon Reduction for Oscillons

In the present work we examine the dynamics of a model for oscillons in 1-dimensional spacetime field theories with a cubic nonlinearity. We utilize a reduction of the model to first and third harmonics, which leads to a reduced partial differential equation (PDE) system whose steady states are candidates for the original PDE oscillons. We analyze the steady states of this model and their stability, including via tools such as index theory. We develop suitable functionals needed for the study of such stationary states, as well as an analogue of the famous Vakhitov-Kolokolov criterion for a quantity whose change of monotonicity reflects a change of stability. Then, we test the relevant predictions, over the full range of oscillon frequencies, through systematic numerical computations of both the reduced model, its steady states and stability, and also of the original PDE model, identifying its time-periodic oscillon solution. Our results yield some significant connections with previous studies, but also some fundamental new insights both on the reduced system and the dynamics of the original system.

nlin.PS↗

arXiv2025

Generic transverse stability of kink structures in atomic and optical nonlinear media with competing attractive and repulsive interactions

We demonstrate the existence and stability of one-dimensional (1D) topological kink configurations immersed in higher-dimensional bosonic gases and nonlinear optical setups. Our analysis pertains, in particular, to the two- and three-dimensional extended Gross-Pitaevskii models with quantum fluctuations describing droplet-bearing environments but also to the two-dimensional cubic-quintic nonlinear Schrödinger equation containing higher-order corrections to the nonlinear refractive index. Contrary to the generic dark soliton transverse instability, the kink structures are generically robust under the interplay of low-amplitude attractive and high-amplitude repulsive interactions. A quasi-1D effective potential picture dictates the existence of these defects, while their stability is obtained numerically and analytically through linearization analysis and direct dynamics in the presence of external fluctuations showcasing their unprecedented resilience. These generic (across different models) findings should be detectable in current cold atom and optics experiments, offering insights towards controlling topological excitations.

cond-mat.quant-gas↗