Related papers: Controversy on a dispersion relation for MHD waves
To describe highly heterogeneous systems using the Cahn-Hilliard equation, the standard form of the thermodynamic potential with a constant coefficient in the gradient term and a polynomial of the fourth degree may not be sufficient. The…
The notion of multipolynomials was recently introduced and explored by T. Velanga in [10] as an attempt to encompass the theories of polynomials and multi- linear operators. In the present paper we push this subject further, by proving…
We study the well-posedness of the initial value problem on periodic intervals for linear and quasilinear evolution equations for which the leading-order terms have three spatial derivatives. In such equations, there is a competition…
We prove dispersive estimates for solutions to the wave equation with a real-valued potential $V\in L^\infty({\bf R}^n)$, $n\ge 4$, satisfying $V(x)=O(|x|^{-(n+1)/2-\epsilon})$, $|x|>1$, $\epsilon>0$.
Under the traveling wave transformation, Camassa-Holm equation with dispersion is reduced to an integrable ODE whose general solution can be obtained using the trick of one-parameter group. Furthermore combining complete discrimination…
The wave equation for spinless particles with the Lorentz violating term is considered. We formulate the third-order in derivatives wave equation leading to the modified dispersion relation. The first-order formalism is considered and the…
Sharp upper and lower bounds are established for the modes of the Poisson distribution of order k. The lower bound established in this paper is better than the previously established lower bound. In addition, for k = 2, 3, 4, 5, a recent…
It is shown that fifth-order nonlinear dispersion equations from compacton theory admit shock and rarefaction waves. A self-similar gradient blow-up is shown to admit infinitely many similarity extensions beyond blow-up time, meaning…
We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding…
A new derivation is given for the representation, under certain conditions, of the integral dispersion relations of scattering theory through local forms. The resulting expressions have been obtained through an independent procedure to…
Integral and derivative dispersion relations (DR) are considered for the $pp$ and $\bar pp$ forward scattering amplitudes. A new representation for the derivative DR, valid at lower energies than the standard one, is obtained. The data on…
The Proton Radius Puzzle refers to the ~7{\sigma} discrepancy that exists between the proton charge radius determined from muonic hydrogen and that determined from electronic hydrogen spectroscopy and electron-proton scattering. One…
This article is devoted to the mass-less energy critical Maxwell-Klein-Gordon system in 4+1 dimensions. In earlier work of the second author, joint with Krieger and Sterbenz, we have proved that this problem has global well-posedness and…
For any kind of wave phenomenon one can find ways to derive the respective dispersion relation from experimental observations and measurements. This dispersion relation determines the structure of the wave equation and thus characterizes…
In this paper, we investigate an electrodynamics in which the physical modes are coupled to a Lorentz-violating (LV) background by means of a higher-derivative term. We analyze the modes associated with the dispersion relations (DRs)…
A perturbative scheme is applied to calculate corrections to the leading, exponentially small (beyond-all-orders) amplitude of the ``trailing'' wave asymptotics of weakly localized solitons. The model considered is a Korteweg-de Vries…
The relativistic second-order corrections at orders $m\alpha^6$ and $m\alpha^6(m/M)$ in hydrogen molecular ions are calculated. Convergence of numerical results is studied, which allows estimating the relative numerical uncertainty to be…
It is shown that the generalized discrete nonlinear Schr\"odinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless…
We consider the radial free wave equation in all dimensions and derive asymptotic formulas for the space partition of the energy relative to a light cone, as time goes to infinity. We show that the exterior energy estimate, which…
Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of…