Related papers: Fractional dynamics in nonlinear magnetic metamate…
The influence of various kinetic effects (e.g. Landau damping, diffusive and collisional dissipation, and finite Larmor radius terms) on the nonlinear evolution of finite amplitude Alfvenic wave trains in a finite-beta environment is…
Local expansion exponents for nonequilibrium dynamical systems, described by partial differential equations, are introduced. These exponents show whether the system phase volume expands, contracts, or is conserved in time. The ways of…
We analyzed conditions for Hopf and Turing instabilities to occur in two-component fractional reaction-diffusion systems. We showed that the eigenvalue spectrum and fractional derivative order mainly determine the type of instability and…
The paper is devoted to the theoretical investigation of the magnetodipolar interparticle interaction effect on remagnetization dynamics in moderately concentrated ferrofluids. We consider a homogeneous (without particle aggregates)…
We investigate theoretically the spiral staircase Heisenberg spin-$1/2$ ladder in the presence of antiferromagnetic long-range spin interactions and a uniform magnetic field. As a special case we also consider the Kondo necklace model. If…
The contribution of the polarization associated with the noncollinear parts of spins in the dielectric permeability tensor of multiferroic materials is considered. As the equilibrium state, we consider the systems of parallel spins, so we…
Our investigation focuses on the asymptotic spreading behavior of the Fisher-KPP equation with a mixed local-nonlocal operator in the diffusion (see the work by X. Cabr\'e and J.-M. Roquejoffre, 2013, ref.[8]) to the setting of mixed…
This paper introduces a generalized fractional Halanay-type coupled inequality, which serves as a robust tool for characterizing the asymptotic stability of diverse time fractional functional differential equations, particularly those…
We study longitudinal and transverse wave propagation in beams with elastic properties that are periodically varying in space and time. Spatiotemporal modulation of the elastic properties breaks mechanical reciprocity and induces one-way…
Time evolution of a nonequilibrium polariton condensate has been studied in the framework of a microscopic approach. It has been shown that due to polariton-polariton scattering a significant condensate depletion takes place in a…
This paper is devoted to the study of the well-posedness of a singular nonlinear fractional pseudo-hyperbolic system. The fractional derivative is described in Caputo sense. The equations are supplemented by classical and nonlocal boundary…
Magnetization of a ferromagnetic substance in response to an externally applied magnetic field increases with the strength of the field. This is because at the microscopic level, magnetic moments in certain regions or domains of the…
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their dynamics. The class of PDEs we focus on are reaction-diffusion equations but we also…
Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated…
Fast magnetic reconnection is defined by the topology of the magnetic field lines changing on a timescale that is approximately an order of magnitude longer than the topology-conserving ideal-evolution timescale. Fast reconnection is an…
In the present work we explore features of single and pairs of solitary waves in a fractional variant of the nonlinear Schr{\"o}dinger equation. Motivated by the recent experimental realization of arbitrary fractional exponents, upon…
We study the process of dispersion of low-regularity solutions to the Schr\"odinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get a lower bound…
We study the effects of quantum fluctuations and the excitation spectrum for the antiferromagnetic Heisenberg model on a two-dimensional quasicrystal, by numerically solving linear spin-wave theory on finite approximants of the octagonal…
We derive the nonlinear fractional surface wave equation that governs compression waves at an interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective…
The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in…