Modulational Instability in Equations of KdV Type

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic

The S2 VLBI System

The S2 VLBI system is described in some detail, including the S2 data acquisition system, data recorder & playback terminals, and the correlator. 1 Introduction The S2 VLBI system is a low cost, high performance, end-to-end VLBI system recently developed in Canada for general research applications including radio astrophysics and astrometry, geodesy and geodynamics, and space VLBI. It consists of the S2 VLBI Data Acquisition System (S2-DAS), the S2 VLBI Data Record Terminal (S2-RT), the S2 VLBI Data Playback Terminal (S2PT) , and the S2 VLBI correlator. The S2 VLBI system includes enhancements such as the S2 Tape-to-Computer Interface (S2-TCI) which enables a direct interface between the S2 recorded baseband samples and a computer memory and associated disk storage. S2-TCI is intended for applications to pulsar research and remote sensing. Preprint submitted to Elsevier Science 27 February Through the use of the S2 VLBI System Interface Adapter (S2-VIA) the S2RT can be interfaced at ..