We demonstrate the pulse compression at 1554 nm using one stage of highly anomalous dispersive photonic crystal fibers with a dispersion value of 600 ps/nm∙km. A 1.64 ps pulse is compressed down to 0.357 ps with a compression factor of 4.6, which agrees reasonably well with the simulation value of 6.1. The compressor is better suited for high energy ultra-short pulse compression than convention...

We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L related norms, with dispersive estimates, which give decay in L∞. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.

We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L related norms, with dispersive estimates, which give decay in L∞. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.