Related papers: Stabilization of localized structures by inhomogen…
The long-term behavior of a modulationally unstable conservative nonintegrable system is known to be characterized by the soliton turbulence self-organization process. We consider this problem in the presence of a long-range interaction in…
Localised radial patterns have been observed in the vegetation of semi-arid ecosystems, often as localised patches of vegetation or in the form of `fairy circles'. We consider stationary localised radial solutions to a reduced model for…
Under non-equilibrium conditions, bosonic modes can become dynamically unstable with an exponentially growing occupation. On the other hand, topological band structures give rise to symmetry protected midgap states. In this letter, we…
Domain specific localization of eigenstates has been a persistent observation for systems with local symmetries. The underlying mechanism for this localization behaviour has however remained elusive. We provide here an analysis of locally…
We report on numerical predictions and experimental observations of a novel type of temporal localized dissipative structures that manifest themselves in the self-defocusing regime of driven nonlinear optical resonators with two…
Networks of nonlocally coupled leaky Integrate-and-Fire neurons exhibit a variety of complex collective behaviors, such as partial synchronization, frequency or amplitude chimeras, solitary states and bump states. In particular, the bump…
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile.…
The FitzHugh-Nagumo model, originally introduced to study neural dynamics, has since found applications across diverse fields, including cardiology and biology. However, the formation and bifurcation structure of spatially localized states…
Self-assembly driven by phase separation coupled to Coulombic interactions is fundamental to a wide range of applications, examples of which include soft matter lithography via di-block copolymers, membrane design using polyelectrolytes,…
Spatially localized oscillations in periodically forced systems are intriguing phenomena. They may occur in spatially homogeneous media (oscillons), but quite often emerge in heterogeneous media, such as the auditory system, where localized…
Training stability is typically regarded as a prerequisite for reliable optimization in large language models. In this work, we analyze how stabilizing training dynamics affects the induced generation distribution. We show that under…
This paper aims at investigating the existence of localized stationary waves in the shallow subsurface whose constitutive behaviour is governed by the hyperbolic model, implying non-polynomial nonlinearity and strain-dependent shear…
Necking instabilities, in which tensile (extensional) deformation localizes into a small spatial region, are generic failure modes in elasto-viscoplastic materials. Materials in this very broad class --- including amorphous, crystalline,…
We theoretically investigate the dynamics, bifurcation structure and stability of quadratic dark localized dissipative states arising in cavity enhanced second-harmonic generation. These states, formed through the locking of plane front…
Local linear instability refers to the linearized discrete operator exhibiting perturbation growth exceeding that of the corresponding continuous linearized problem. In the context of nonlinear entropy-stable discretizations, we argue that…
The Eckhaus instability is a secondary instability of nonlinear spatiotemporal patterns in which high-wavenumber periodic solutions become unstable against small-wavenumber perturbations. We show in this letter that this instability can…
Isospectral transformations of exactly solvable models constitute a fruitful method for obtaining new structures with prescribed properties. In this paper we study the stability group of the Dirac algebra in honeycomb lattices representing…
A quiet point, an operating point of pump-resonance detuning that minimizes frequency fluctuation due to nonlinear effects inside a resonator, has been employed for phase noise reduction of a soliton Kerr microresonator frequency comb…
Dissipative structures are the result of spontaneous symmetry breaking in a dynamic open system, which is induced by either the nonlinear effect or loss fluctuations. While optical temporal dissipative solitons in nonlinear Kerr cavities…
We study local radiation magnetohydrodynamic instabilities in static, optically thick, vertically stratified media with constant flux mean opacity. We include the effects of vertical gradients in a horizontal background magnetic field.…