# gst: multi-ring necklace vortex solitons in Kerr nonlinear media with azimuthally modulated Bessel potentials.

<< ️(AA) address the existence, stability, and dynamics of single-ring and multi-ring vorticity-carrying necklace solitons under the action of the Kerr nonlinearity and a Bessel-lattice potential modulated in the azimuthal direction. The model may be realized in the spatial domain for bulk optical waveguides, the spatiotemporal domain for optical cavities, and for effectively two-dimensional Bose-Einstein condensates. The setup supports single- and multi-ring necklace vortex patterns, including monopoles, dipoles, tripoles, quadrupoles, pentapoles, sextupoles, octupoles, and 12-poles. >>

<< ️In contrast with the inherent instability of conventional vortex beams with high topological charges (winding numbers), vortex necklace-shaped solitons with large winding numbers are found to be stable in the present setup. In particular, octupoles exhibit stable breathing dynamics, and 12-pole necklaces with high winding numbers may be stable. >>

<< ️These (AA) findings provide a new way for generating stable vortex necklaces, offering a vast potential for manipulations of complex spatiotemporal light fields. >>

Ruolan Zhao, Jing Chen, Boris A. Malomed, et al. Multi-ring necklace vortex solitons in Kerr nonlinear media with azimuthally modulated Bessel potentials. arXiv: 2602.18703v1 [physics.optics]. Feb 21, 2026.

https://arxiv.org/abs/2602.18703

Also: vortex, soliton, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, solitons, vortex necklace-shaped solitons, single-ring vorticity, multi-ring vorticity, stable vortex necklace, transitions.

# gst: superflows around corners.

<< ️(AA) investigate analytically and numerically the dynamics of a two-dimensional superflow governed by the Gross-Pitaevskii equation passing over finite-size rectangular obstacles: an impenetrable wall and an impenetrable rectangular well. Extending classical studies of vortex nucleation around smooth obstacles, (They) focus on the role of sharp corners in determining the onset of vortex nucleation. Using a combination of analytical techniques based on the Schwarz-Christoffel methods for potential flow and on numerical simulations, (They) show that local velocity amplification near sharp corners crucially controls the critical flow velocity for vortex nucleation. >>

<< ️For both wall and well configurations, (They) identify analytically and theoretically the critical velocities as a function of the obstacle width and its height or depth, finding an excellent agreement between the theory and (Their) numerical simulations. (Their) results provide a simple framework for understanding superflow stability past finite-size obstacles with sharp features and are directly relevant to experimentally realizable configurations in atomic Bose-Einstein condensates and related superfluid systems. >>

Thomas Frisch, Christophe Josserand, Sergio Rica. Superflows around corners. arXiv: 2602.18876v1 [cond-mat.quant-gas]. Feb 21, 2026.

https://arxiv.org/abs/2602.18876

Also: vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vorticity, vortex nucleation, two-dimensional superflow, superflow stability, smooth obstacles, sharp corners. 

# gst: a phase description of mutually coupled chaotic oscillators.

<< ️The synchronization of rhythms is ubiquitous in both natural and engineered systems, and the demand for data-driven analysis is growing. When rhythms arise from limit cycles, phase reduction theory shows that their dynamics are universally modeled as coupled phase oscillators under weak coupling. This simple representation enables direct inference of inter-rhythm coupling functions from measured time-series data. >>

<< ️However, strongly rhythmic chaos can masquerade as noisy limit cycles. In such cases, standard estimators still return plausible coupling functions even though a phase-oscillator model lacks a priori justification. >>

<< ️(AA) therefore extend the phase description to the chaotic oscillators. Specifically, (They) derive a closed equation for the phase difference by defining the phase on a Poincaré section and averaging the phase dynamics over invariant measures of the induced return maps. Numerically, the derived theoretical functions are in close agreement with those inferred from time-series data. Consequently, (Their) results justify the applicability of phase description to coupled chaotic oscillators and show that data-driven coupling functions retain clear dynamical meaning in the absence of limit cycles. >>

Haruma Furukawa, Takashi Imai, Toshio Aoyagi. A Phase Description of Mutually Coupled Chaotic Oscillators. arXiv: 2602.17519v1 [nlin.CD]. Feb 19, 2026.

https://arxiv.org/abs/2602.17519

Also: chaos, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, synchronization of rhythms, limit cycles, noisy limit cycles, coupled phase oscillators, transitions.

# gst: spatiotemporal noise stabilizes unbounded diversity in strongly-competitive communities.

<< ️Classical ecological models predict that large, diverse communities should be unstable, presenting a central challenge to explaining the stable biodiversity seen in nature. (AA) revisit this long-standing problem by extending the generalized Lotka-Volterra model to include both spatial structure and environmental fluctuations across space and time.  >>

<< ️(They) find that neither space nor environmental noise alone can resolve the tension between diversity and stability, but that their combined effects permit arbitrarily many species to stably coexist despite strongly disordered competitive interactions. (They) analytically characterize the noise-induced transition to coexistence, showing that spatiotemporal noise drives an anomalous scaling of abundance fluctuations, known empirically as Taylor's law. >>

<< ️At the community level, this manifests as an effective sublinear self-inhibition that renders the community stable and asymptotically neutral in the high-diversity limit. Spatiotemporal noise thus provides a novel resolution to the diversity-stability paradox and a generic mechanism by which complex communities can persist. >>

Amer Al-Hiyasat, Daniel W. Swartz, Jeff Gore, et al. Spatiotemporal noise stabilizes unbounded diversity in strongly-competitive communities. arXiv: 2602.13423v1 [q-bio.PE]. Feb 13, 2026.

https://arxiv.org/abs/2602.13423

Also: noise, disorder, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, noise, spatiotemporal noise, disorder, transition, noise-induced transition, disordered competitive interactions, spatial structure and environmental fluctuations.

# gst: dynamics of perturbed elliptical billiard tables.

<< ️Dynamical billiards consist of a particle on a two-dimensional table, bouncing elastically off a boundary curve. The state of the system is given by two numbers: one describing the location along the curve where the bounce occurs, and another describing the incoming angle of the bounce. Successive bounces define a two-dimensional area preserving map, and iterating this map gives a dynamical system first studied by Birkhoff. >>

<< ️One of the simplest smooth table shapes is that of an ellipse, in which case the dynamics of the billiard map is completely integrable. The longstanding Birkhoff conjecture is that elliptical tables are the only smooth convex table for which complete integrability occurs. >>

<< ️In this spirit, (AA) present an implicit real analytic method for iterating billiard maps on perturbed elliptical tables. This method allows (They) to compute local stable and unstable manifolds of periodic orbits using the parameterization method. Globalizing these local manifolds numerically provides insight into the dynamics of the table. >>

Patrick Bishop, Summer Chenoweth, Emmanuel Fleurantin, et al. Dynamics of perturbed elliptical billiard tables. arXiv: 2602.15272v1 [math.DS]. Feb 17, 2026.

https://arxiv.org/abs/2602.15272

Also: billiard, particle, bouncing, elastic, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, billiard, particles, bouncing, elasticity, perturbed elliptical table.

# gst: steady states in a model of opposing local and nonlocal hops.

<< ️(AA) study a one-dimensional lattice model of particles following hard-core exclusion and performing opposing local and nonlocal moves with probability 𝑝 and 1−𝑝, respectively. (Their) model shows the interesting feature that the direction of the particle current can be switched by simply changing the density 𝜌 of particles on the lattice. (They) study the dependence of current on 𝑝 as well as 𝜌 and present the separation of positive and negative current regions on a 𝑝−𝜌 plane. >>

<< ️Further, (They) study the effect of disorder on this model by introducing a single site with valvelike dynamics. The site allows only unidirectional, local outward motion with rate 𝑟. The interplay of the disorder strength 𝑟, particle density 𝜌, and probability 𝑝 leads to a rich possibility with four different kinds of shock phases in the steady state. >>

<< ️(They) study the shock densities using Monte Carlo simulations and mean field calculations. While (Their) mean field treatment describes the numerical results quite well qualitatively, (AA) see certain quantitative deviations. (They) try to understand these deviations using measures of correlation in the system and provide heuristic arguments for the mismatch. >>

Ankur Mishra, Apoorva Nagar. Steady states in a model of opposing local and nonlocal hops. Phys. Rev. E 113, 024113. Feb 10, 2026.

https://journals.aps.org/pre/abstract/10.1103/66lp-n7hv

Also: particle, disorder, transitions, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, disorder, phase transitions, shock phases, valvelike dynamics.

# gst: phase-controlled elastic, inelastic, and coalescent collisions of two-dimensional flat-top solitons.

<< ️(AA) investigate elastic, inelastic, and coalescent collisions between two-dimensional flat-top solitons supported by the cubic-quintic nonlinear Schrödinger equation. Numerical simulations reveal distinct collision regimes ranging from nearly elastic scattering to strongly inelastic interactions leading to long-lived merged states. >>

<< ️(They) demonstrate that the transition between these regimes is primarily controlled by the relative phase of the solitons at the collision point, with out-of-phase collisions suppressing overlap and in-phase collisions promoting strong interaction. >>

<< ️Kinetic-energy diagnostics are introduced to quantitatively characterize collision outcomes and to identify phase- and separation-dependent windows of elasticity. To interpret the observed dynamics, (They) extract effective phase-dependent interaction potentials from collision trajectories, providing a mechanical picture of attraction and repulsion between flat-top solitons. The stability of merged states formed after strongly inelastic collisions is explained by their lower energetic cost, arising from interfacial energetics, where a balance between internal pressure and edge tension plays a central role. A variational analysis based on direct energy minimization supports this picture by revealing robust energetic minima associated with stationary two-dimensional flat-top solitons. >>

M. O. D. Alotaibi, Y. O. A. Abughnheim, L. Al Sakkaf, et al. Phase-controlled elastic, inelastic, and coalescent collisions of two-dimensional flat-top solitons. arXiv: 2602.07762v1 [nlin.PS]. Feb 8, 2026.

https://arxiv.org/abs/2602.07762

Also: soliton, elastic, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, soliton, transitions, elastic, inelastic, and coalescent collisions, elastic scattering interactions, strongly inelastic interactions, long-lived merged states, attraction, repulsion, internal pressure, edge tension.