Modulational Instability of Fast Sausage Mode as One of the Possible Mechanisms for Quasiperiodic Pulsations during Solar Flares

Quasiperiodic pulsations (QPPs) are frequently observed in the entire range of the electromagnetic spectrum during solar flares, and there can be many possible mechanisms leading to this phenomenon. In the present work, we demonstrate the possibility of the generation of QPPs by a nonlinear fast sausage mode in a coronal loop. The coronal loop itself is represented by an infinitely long homogenous magnetic flux tube, which in many cases is a good approximation, and the nonlinearity of the fast sausage mode is modeled by the nonlinear Schrödinger equation (NSE) with a cubic nonlinearity. We have shown that the frequency-renormalized plane wave solution, which happens to be an exact solution of the NSE, transforms into a series of quasiperiodic oscillations (QPOs) due to the so-called modulational instability or the Benjamin–Feir instability. Our numerical solutions show that such QPOs evolve at almost every point above a certain height along the magnetic flux tube, which represents the coronal loop. As the fast sausage mode perturbs the plasma density strongly, the density perturbations caused by the QPOs of the nonlinear fast sausage mode correspondingly modulate the radiation throughout the electromagnetic spectrum, resulting in the emergence of the corresponding QPPs. This mechanism should therefore be able to describe some of the observed QPPs.

Efficient Fourier-collocation method for full scattering data of Zakharov-Shabat periodic problem

<p>The one-dimensional nonlinear Schrodinger equation (NLSE) serves as a universal model of nonlinear wave propagation appearing in different areas of physics. In particular it describes weakly nonlinear wave trains on the surface of deep water and captures up to certain extent the phenomenon of rogue waves formation. The NLSE can be completely integrated using the inverse scattering transform method that allows transformation of the wave field to the so-called scattering data representing a nonlinear analogue of conventional Fourier harmonics. The scattering data for the NLSE can be calculated by solving an auxiliary linear system with the wave field playing the role of potential – the so-called Zakharov-Shabat problem. Here we present a novel efficient approach for numerical computation of scattering data for spatially periodic nonlinear wave fields governed by focusing version of the NLSE. The developed algorithm is based on Fourier-collocation method and provides one an access to full scattering data, that is main eigenvalue spectrum (eigenvalue bands and gaps) and auxiliary spectrum (specific phase parameters of the nonlinear harmonics) of Zakharov-Shabat problem. We verify the developed algorithm using a simple analytic plane wave solution and then demonstrate its efficiency with various examples of large complex nonlinear wave fields exhibiting intricate structure of bands and gaps. Special attention is paid to the case when the wave field is strongly nonlinear and contains solitons which correspond to narrow gaps in the eigenvalue spectrum, see e.g. [1], when numerical computations may become unstable [2]. Finally we discuss applications of the developed approach for analysis of numerical and experimental nonlinear wave fields data.</p><p>The work was supported by Russian Science Foundation grant No. 20-71-00022.</p><p>[1] A. A. Gelash and D. S. Agafontsev, Physical Review E 98, 042210 (2018).</p><p>[2] A. Gelash and R. Mullyadzhanov, Physical Review E 101, 052206 (2020).</p>

Semi-exact local absorbing boundary condition for seismic wave simulation

An absorbing boundary condition is necessary in seismic wave simulation for eliminating the unwanted artificial reflections from model boundaries. Existing boundary condition methods often have a trade-off between numerical accuracy and computational efficiency. We proposed a local absorbing boundary condition for frequency-domain finite-difference modelling. The proposed method benefits from exact local plane-wave solution of the acoustic wave equation along predefined directions that effectively reduces the dispersion in other directions. This method has three features: simplicity, accuracy and efficiency. Numerical simulation demonstrated that the proposed method has higher efficiency than the conventional methods such as the second-order absorbing boundary condition and the perfectly matched layer (PML) method. Meanwhile, the proposed method shared the same low-cost feature as the first-order absorbing boundary condition method.

Exact plane-wave solution of equations of gravitation theory with massive graviton

The theory of gravitation with a massive graviton, which was proposed by Visser, is considered. The exact solution of this theory is found when the source of the gravitational field is plane scalar wave. The Hamilton-Jacobi method obtained the laws of motion of massive and massless particles in this gravitational field.

Linear peridynamics for triclinic materials

The governing equation of linear peridynamics is developed for the most general anisotropic materials (triclinic materials). As a departure from the standard peridynamic theory, the linear constitutive equation in the form of a micromodulus is determined by directly requiring the resulting peridynamic equation to converge to a comparable classical elastodynamic equation for a triclinic material as the generalized material horizon approaches zero. As a result, a new peridynamic governing equation is obtained for triclinic peridynamic materials. As an application of the newly obtained peridynamic equation, a plane wave solution is analytically obtained and discussed, and dispersion curves are plotted for triclinic peridynamic materials.

Gravitational waves in massive conformal gravity

First, we obtain the plane wave solution of the linearized massive conformal gravity field equations. It is shown that the theory has seven physical plane waves. In addition, we investigate the gravitational radiation from binary systems in massive conformal gravity. We find that the theory with large graviton mass can reproduce the orbit of binaries by the emission of gravitational waves.

Breathers, rogue waves and their dynamics in a (2+1)-dimensional nonlinear Schrödinger equation

Under investigation in this paper is a (2[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Schrödinger equation, which is a generalization of the standard nonlinear Schrödinger equation. By means of the modified Darboux transformation, the hierarchies of rational solutions and breather solutions are generated from the plane wave solution. Furthermore, the main characteristics of the nonlinear waves including the Akhmediev breathers, Kuznetsov–Ma solitons, and their combined structures are graphically discussed. Our results would be of much importance in enriching and explaining rogue wave phenomena in nonlinear wave fields.

Polarization

This chapter discusses the polarization of light, including the transverse nature of the plane-wave solution; the linear and circular bases are introduced, and the propagation of polarized light in media is analysed.