W-Gleitgleitkinematik

The following gives some starting elements of a theory, which the author calls glide-glide-kinematics and which goes far beyond the kinematics of helical motion in ℝ ⁿ , which was studied up to now. We are mainly concerned here with “angle-preservering glide-glide-kinematics”, generalising (and giving as well some idea of) the distance-preservering glide-glide-kinematics, which we develop in a forthcoming book ([5]) in detail.      

From X- to O-shaped spatiotemporal spectra of light filaments in water

We show that the angle-wavelength spectra of light filaments excited by ultrashort pulses experience a transition from X- to O-like structures when their carrier wavelengths are switched from normal to anomalous dispersion. Calculations confirm that the O-shaped conical emission follows the elliptic geometry of the nonlinear Schr?dinger equation with anomalous dispersion.