相关论文: Controversy on a dispersion relation for MHD waves
Pandey & Dwivedi (2007) again tried to claim that the dispersion relation for the given set of equations must be a sixth degree polynomial. Through a series of papers, they are unnecessarily creating confusion. In the present communication,…
We consider viscosity and thermal conductivity as dissipation mechanisms to derive a general dispersion relation for MHD waves propagating in a homogeneous plasma. We show that the actual dispersion relation for MHD waves in a homogeneous…
Considering thermal conduction, compressive viscosity and optically thin radiation as damping mechanisms for MHD waves, we derive a six-order general dispersion relation. We point out a fundamental flaw in the derivation of five-order…
Chandra [1] made an attempt to show that the work of Dwivedi and Srivastava [2] (hereinafter DS) can be investigated even analytically and their results are erroneous. Dwivedi and Srivastava [3] picked up some values of Chandra [1] and…
We comment on the recent paper by Srivastava and Dwivedi (J. Astrophs. Astr. {\bf 28}, 1, 2007). In the said paper the derived dispersion relation $\nu \eta \cos^4 \theta k^4 + [v_A^2 - i \omega (\nu + \eta)] \cos^2 \theta k^2 - \omega^2 =…
We comment on the work by Chandra and Kumthekar (2007, henceforth CK) which is questionable. In the derivation of dispersion relation, CK neither invoke the concept of vector space nor do they follow the basic criterion for the elimination…
The authors of the paper "The third-order perturbed Korteweg-de Vries equation for shallow water waves with a non-flat bottom" [1] claim that they have derived the full third order perturbed KdV equation for the case of uneven bottom. We…
In a frame of quasi-crystal approximation the dispersion equations are obtained for the wave vector of a coherent electromagnetic wave propagating in a media which contains a random set of parallel dielectric cylinders with possible…
We consider the Cauchy problem for the fifth-order modified Korteweg-de Vries equation (mKdV) under the periodic boundary condition. The fifth-order mKdV is an asymptotic model for shallow surface waves, and (in the perspective of…
We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and…
Inspired by the fundamental work of Escobedo and Velazquez \cite{EscobedoVelazquez:2015:FTB,EscobedoVelazquez:2015:OTT}, we prove that solutions of 4-wave kinetic equations, under very general forms of the dispersion relations, exhibit the…
The dispersion equation of MGD plasma waves measured in a reference frame with a relative speed from that where they are generated is derived. The analysis leads further from what is known for waves produced in stationary plasmas in the…
The Dirac equation with Lorentz violation involves additional coefficients and yields a fourth-order polynomial that must be solved to yield the dispersion relation. The conventional method of taking the determinant of $4\times 4$ matrices…
The usual pre-metric Maxwell equations of electromagnetism in Minkowski space are extended to five dimensions, and the equations of linear five-dimensional electromagnetic waves are obtained from them by using the simplest electromagnetic…
The purpose of this note is to prove dispersive estimates for the wave equation outside a ball in R^d. If d = 3, we show that the linear flow satisfies the dispersive estimates as in R^3. In higher dimensions d $\ge$ 4 we show that losses…
The process of wave propagation in an infinite linear chain is analyzed. Established, that dispersion relation between the angular frequency and the wave number for transverse waves differs from similar dependencies for longitudinal.
A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of…
In this paper, we derive a dispersion relation for sound waves in viscous and heat conducting fluids. In particular this dispersion (i.e. variation of speed of sound with frequency) is shown to be of second order of magnitude, w.r.t.…
An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential…
We study amplitudes of five-wave interactions for evolution Hamiltonian equations differ from the KdV equation by the form of dispersion law. We find that five-wave amplitude is canceled for all three known equations (KdV, Benjamin-Ono and…