We study the two and three dimensional, N = 2, 3, nonlinear dispersive equation CN (m, a + b): ut + (u )x + [ ua∇2ub] x = 0 where the degeneration of the dispersion at ground state induces cylindrically and spherically symmetric compactons convected in x-direction. An initial pulse of bounded extent decomposes into a sequence of robust compactons. Colliding compactons seem to emerge from the in...

Scanning electron microscopy with energy-dispersive X-ray spectrometry (SEM-EDS) was used to characterize a macroscopic artifact from Peru (a Moche cast figure) [1]. A 3D hyperspectral datacube was acquired over 51.2 hours, measuring 11,520 x 9,984 pixels with 2,048 energy channels per pixel; each pixel corresponds to 900 nm in the x and y dimensions. With current technology, interacting with t...

We prove a dispersive estimate for the time-independent Schrödinger operator H = −∆ + V in three dimensions. The potential V (x) is assumed to lie in the intersection L(R) ∩ L(R), p < 3 2 < q, and also to satisfy a generic zero-energy spectral condition. This class, which includes potentials that have pointwise decay |V (x)| ≤ C(1+ |x|)−2−ε, is nearly critical with respect to the natural scalin...

We study the two and three dimensional, N=2, 3, nonlinear dispersive equation CN(m,a+b): u(t)+(u(m))x + [u(a)inverted delta2ub]x=0 where the degeneration of the dispersion at the ground state induces cylindrically and spherically symmetric compactons convected in the x direction. An initial pulse of bounded extent decomposes into a sequence of robust compactons. Colliding compactons seem to eme...