In this paper, we consider the spectral stability of spatially periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long-wavelength perturbations. Specifically, we extend the work of Bronski and Johnson by demonstrating that the homogenized system describing the mean behavior of a slow modulation (WKB) approximation of the solution correctly describes the linearize...

RICE et ml. (1994, J. Mech. Ph_vs. Solids 42, 813-843) analyse the propagation of a planar crack with a nominally straight front in a model elastic solid with a single displacement component. Using the form of their results for a strictly linearized perturbation from a straight crack front which moves at uniform speed, we give the corresponding first-order expression for the deviation of a crac...

Subsurface rock properties are manifested in seismic records as variations in traveltimes, amplitudes, and waveforms. It is commonly acknowledged that traveltimes are sensitive to the long wavelength part of the velocity, whereas amplitudes are sensitive to the short wavelength part of the velocity. The inherent sensitivity of seismic velocity at different wavelengths suggests an approach that ...

The authors explore the use of the ‘‘neutral vectors’’ of a linearized version of a global quasigeostrophic atmospheric model with realistic mean flow in the study of the nonlinear model’s low-frequency variability. Neutral vectors are the (right) singular vectors of the linearized model’s tendency matrix that have the smallest eigenvalues; they are also the patterns that exhibit the largest re...

We construct a class of knot solutions the gravitoelectromagnetic (GEM) equations in vacuum linearized gravity approximation by analogy with Ra\~{n}ada-Hopf fields. For these solutions, dual metric tensors bi-metric geometry gravitational perturbations are given and geodesic equation as function two complex parameters GEM knots calculated. Finally, Landau--Lifshitz pseudo-tensor scalar invarian...

Abstract We present a three-dimensional (3D) numerical solver of the linearized compressible Euler equations (Global Acoustic Linearized Euler), used to model acoustic oscillations throughout solar interior. The governing are solved in conservation form on fully global spherical mesh (0 ? ? 2 ? , 0 ? r R ? ) over background state generated by standard S. implement an efficient pseudospectral co...

Intermediate models of the coupled tropical atmosphere-ocean system have been used to illuminate the physics of interannual climate phenomenon such as El Niño – Southern Oscillation (ENSO) in the tropical Pacific and to explore how the tropics might respond to an forcing such as changing insolation (Milankovitch) or atmospheric carbon dioxide. Importantly, most of the intermediate models are co...

We study the long time asymptotic behavior of inviscid magnetohydrodynamic equations with magnetic dissipation near a combination Couette flow and constant field. Here we show that there exist nearby explicit global in low frequency solutions, which call waves. Moreover, linearized problem around these waves exhibits resonances under high perturbations, called echoes, result norm inflation Gevr...

Proof. Suppose π̄ / ∈ Πm,n. Then ∃i, j1 < j2 such that π̄i,(j1)w < π̄i,(j2)w , i.e. such that π̄i,(j1)w = 0 and π̄i,(j2)w = 1. This means that π̄ ranks x + i above x−(j1)w but below x − (j2)w . Now let us construct from π̄ an ordering π̄ in which the instances x−(j1)w and x−(j2)w are swapped, i.e. for all i ′ with π̄i′,(j1)w = 0 and π̄i′,(j2)w = 1, we set π̄ ′ i′,(j1)w = 1 and π̄ i′,(j2)w = 0. Then it can ...

We derive the equations governing linear stability of Kerr–Newman spacetime to coupled electromagnetic-gravitational perturbations. The generalize celebrated Teukolsky equation for curvature perturbations Kerr, and Regge–Wheeler metric Reissner–Nordström. Because “apparent indissolubility coupling between spin-1 spin-2 fields”, as put by Chandrasekhar, cannot be obtained through standard decomp...