相关论文: Controversy on a dispersion relation for MHD waves
D. Dimitrov has posed the problem of finding polynomials that set the sharpness of the Koebe Quarter Theorem for polynomials and asked whether Suffridge polynomials are optimal. We disprove Dimitrov's conjecture for polynomials of degree 3,…
The linear dispersion relation of a finite amplitude, parallel, circularly polarized Alfv\'en wave in a relativistic electron-positron plasma is derived. In the nonrelativistic regime, the dispersion relation has two branches, one…
We discuss the propagation of electromagnetic waves on a rectangular lattice of polarizable point dipoles. For wavelengths long compared to the lattice spacing, we obtain the dispersion relation in terms of the lattice spacing and the…
Channels of energy estimates control the energy of an initial data from that which it radiates outside a light cone. For the linearised energy critical wave equation they have been obtained in the radial case in odd dimensions, first in $3$…
This paper considers the initial value problem for a class of fifth order dispersive models containing the fifth order KdV equation $$\partial_tu - \partial_x^5u - 30u^2\partial_xu + 20\partial_xu\partial_x^2u + 10u\partial_x^3u = 0.$$ The…
We have obtained the perturbative expressions up to sixth order for the energy of the bound state in a one dimensional, arbitrarily weak, short range finite well, applying a method originally developed by Gat and Rosenstein Ref. [3]. The…
In 1978, Apery has given sequences of rational approximations to $\zeta(2)$ and $\zeta(3)$ yielding the irrationality of each of these numbers. One of the key ingredient of Apery's proof are second-order difference equations with polynomial…
Third-order nonlinear dispersion equations (NDEs) are shown to admit both shock and rarefaction waves (as weak solutions), which are distinguished by a smooth deformation approach. Compacton-type travelling wave solutions are proved to be…
The authors of the paper "Two-dimensional third- and fifth-order nonlinear evolution equations for shallow water waves with surface tension" \cite{Fok} claim that they derived the equation which generalizes the KdV equation to two space…
Fifth-order 1D nonlinear dispersion equations are shown to admit blow-up formation of shock waves as well as rarefaction waves. The concepts of smooth deformations are applied to distinguish "entropy" shocks from smooth rarefaction waves.…
The interaction of two colliding Alfv\'en wave packets is here described by means of magnetohydrodynamics (MHD) and hybrid kinetic numerical simulations. The MHD evolution revisits the theoretical insights described by Moffatt, Parker,…
Deviation from standard dispersion relations for electrons and photons in the form of an extra term proportional to an arbitrarily high power of momentum is studied. It is shown that observational constraints lead to a region in the…
In his seminal part IV, Ann. der Phys. Vol 81, 1926 paper, Schrodinger has developed a clear understanding about the wave equation that produces the correct quadratic dispersion relation for matter-waves and he first presents a real-valued…
In this Comment, we refute conclusions made in Phys. Rev. Lett. 112, 233601 (2014) by L.-G. Wang, L. Wang, M. Al-Amri, S.-Y. Zhu, and M. S. Zubairy. These conclusions stem from the use of the linear theory, which is not applicable to…
We discuss some formal and practical aspects related to the replacement of Integral Dispersion Relations (IDR) by derivative forms, without high-energy approximations. We first demonstrate that, for a class of functions with physical…
Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can…
The naive use of higher order perturbation theory leads the left--hand cut integrals in $\pi\pi$ dispersion relations~\cite{hjy,Xiao01} divergent. This problem is discussed and solved. Also we point out that the Adler zero condition imposes…
MHD turbulence consists of waves that propagate along magnetic fieldlines, in both directions. When two oppositely directed waves collide, they distort each other, without changing their respective energies. In weak MHD turbulence, a given…
The possibility of finite-time, dispersive blow up for nonlinear equations of Schroedinger type is revisited. This mathematical phenomena is one of the possible explanations for oceanic and optical rogue waves. In dimension one, the…
The propagation of ON-OFF signals with dispersive waves is examined in this study. An integral-form exact solution for a simple ON-OFF switching event is derived, which holds for any dispersion relation. The integral can be exactly…