Complex short pulse and coupled complex short pulse equations

The Short Pulse Hierarchy

We study a new hierarchy of equations containing the Short Pulse equation, which describes the evolution of very short pulses in nonlinear media, and the Elastic Beam equation, which describes nonlinear transverse oscillations of elastic beams under tension. We show that the hierarchy of equations is integrable. We obtain the two compatible Hamiltonian structures. We construct an infinite serie...

Solitary Waves of the Regularized Short Pulse and Ostrovsky Equations

We derive a model for the propagation of short pulses in nonlinear media. The model is a higher order regularization of the short pulse equation (SPE). The regularization term arises as the next term in the expansion of the susceptibility in derivation of the SPE. Without the regularization term there do not exist traveling pulses in the class of piecewise smooth functions with one discontinuit...

Diiractive Short Pulse Asymptotics for Nonlinear Wave Equations

We present an algorithm for constructing approximate solutions to nonlinear wave propagation problems in which diiractive eeects and nonlinear eeects come into play on the same time scale. The approximate solutions describe the propagation of short pulses. In a separate paper the equations used to construct the approximate solutions are derived using the method of multiple scales and the approx...

High - Intensity Short - Pulse Lasers

Short-pulse laser-produced plasmas

In this review, the physics of short-pulse laser-produced plasmas at moderate intensities is described, together with applications to x-ray sources and material processing.