Laboratory experiments have shown that when nonlinear, dispersive waves are forced periodically from one end of an undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. It is our purpose here to establish this as a fact at least in the context of a damped Korteweg-de Vries equation. Thus, consideration is given to the initial-...

We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L related norms, with dispersive estimates, which give decay in L∞. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.

We study the Whitham equations for the defocusing complex modified KdV (mKdV) equation. These Whitham equations are quasilinear hyperbolic equations and they describe the averaged dynamics of the rapid oscillations which appear in the solution of the mKdV equation when the dispersive parameter is small. The oscillations are referred to as dispersive shocks. The Whitham equations for the mKdV eq...

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I briefly discuss the derivation of dispersive sum rules constraining semileptonic form-factors. I outline the use of these constraints in the context of charmless semileptonic decays and suggest how, in combination with other theoretical and experimental information, they may reduce the uncertainties in the extraction of V ub .

In this paper we establish dispersive estimates for solutions to the linear Schrödinger equation in three dimension 1 i ∂ t ψ − △ψ + V ψ = 0, ψ(s) = f (0.1) where V (t, x) is a time-dependent potential that satisfies the conditions sup t V (t, ·)

This paper concerns the orbital stability and instability of solitary waves of the system of coupling equations of Benjamin-Bona-Mahony type. By applying the abstract results of Grillakis, Shatah and Strauss and detailed spectral analysis, we obtain the existence and stability of the solitary waves.

In this letter we introduce a new method to determine the radiative neutrino decay rate in the presence of a medium. Our approach is based on the generalisation of the optical theorem at finite temperature and density. Differently from previous works on this subject, our method allows to account for dispersive and dissipative electromagnetic properties of the medium. Some inconsistencies that a...

The pointwise behavior of dispersive difference schemes for the simple wave equation in one dimension is analyzed. If the initial data are in certain Besov spaces, the scheme is shown to be pointwise unbounded. Boundedness is shown when the initial data are of bounded variation.