Three-wave interactions (M ↔ P + Q) of plasma waves propagating parallel to the mean magnetic field at frequencies below the electron cyclotron frequency are considered. We consider Alfvén–ion-cyclotron waves (L), fast-magnetosonic–whistler waves (R), and ion-sound waves (I). Especially the weakly turbulent low-beta plasmas like the solar corona are studied, using the cold-plasma dispersion rel...

We discuss the linear dispersive properties of finite one-dimensional photonic band-gap structures. We introduce the concept of a complex effective index for structures of finite length, derived from a generalized dispersion equation that identically satisfies the Kramers-Kronig relations. We then address the conditions necessary for optimal, phase-matched, resonant second harmonic generation. ...

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...

Abstract Based on the recent work [4] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schrödinger operator Hφ = (−∆+ V )φ = −(φn+1 + φn−1 − 2φn) + Vnφn. We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicit...