Dispersive hydrodynamics is the domain of applied mathematics and physics concerned with fluid motion in which internal friction, e.g., viscosity, is negligible relative to wave dispersion. In conservative media such as superfluids, optical materials, and water waves, nonlinearity has the tendency to engender wavebreaking that is mitigated by dispersion. The mathematical framework for such medi...

The paper is devoted to new trends in dispersive control techniques for ultrafast light emission. Acoustooptical dispersive delay lines for controlling the spectral components and phase composition of ultrashort laser pulses are considered. The method of super high frequency modulation of chirped femtosecond laser pulses is proposed. Theoretical approach to dispersive pulse shaping is supported...

We consider in this paper the well-posedness for the Cauchy problem associated to two-dimensional dispersive systems of Boussinesq type which model weakly nonlinear long wave surface waves. We emphasize the case of the strongly dispersive ones with focus on the “KdV-KdV” system which possesses the strongest dispersive properties and which is a vector two-dimensional extension of the classical K...

We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of di↵usion and dispersion are known to give rise to monotonic and oscillatory traveling waves that approximate shock waves. The zero-di↵usion limits of these traveling waves are dynamically expanding dispersive shock waves (DSWs). A r...

In this paper, we study the infinite propagation speed and the limit behavior for the b-family equation with dispersive term. We prove that any nontrivial classical solution of the b-family equation with dispersive term will not have compact support if its initial data has this property. The issue of passing to the limit as the dispersive parameter tends to zero for the solution of the b-family...

A novel concept for octave spanning dispersive mirrors with low spectral dispersion oscillations is presented. The key element of the so-called wedge dispersive mirror is a slightly wedged layer which is coated on a specially optimized dispersive multilayer stack by a common sputter coating process. The group delay dispersion (GDD) of a pulse reflected on a wedge dispersive mirror is nearly fre...

We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system – which we show is essentially ...

The present paper is about Bernstein-type estimates for Jacobi polynomials and their applications to various branches in mathematics. This is an old topic but we want to add a new wrinkle by establishing some intriguing connections with dispersive estimates for a certain class of Schrödinger equations whose Hamiltonian is given by the generalized Laguerre operator. More precisely, we show that ...