Wave breaking in the Short-Pulse Equation
David Trubatch, Montclair State University
About the Seminar
The Short-Pulse Equation (SPE) is a model for ultra-short (pico- and femto-second) pulses in optical fibers with Kerr nonlinearity. The pulse solution of the SPE is known to undergo wave breaking (derivative catastrophe) in finite time when the shortness parameter of the pulse exceeds a threshold value. The appearance of the break is reflected in a qualitative change in the spatial Fourier transform of the solution. Hence, the Fourier data can be used to detect wave breaking in solutions obtained by numerical simulation. For Gaussian-type initial data, the parameter dependence of wave breaking cannot be completely determined analytically. Instead there is a gap in parameter space between a region of solutions that exist for infinite time and solutions known to break in finite time. By analysis of numerically simulated solutions with Gaussian-type initial data, it is possible to identify threshold parameter values inside the theoretically derived gap that separates breaking and non-breaking solutions.