Department of Mathematics
Mathematics in Science & Society
Spring 1999

Homoclinic bifurcation theory gives a mathematical context for constructing multiple pulses that are formed as a concatenation of many, well-separated base pulses. Recent progress has led to a deeper understanding of the stability of pulses found in this way. Within the context of nonlinear optics, application of these methods offers strong suggestions as to the most stabilizing amplification schemes. In contrast, multiple beam solutions of coupled nonlinear Schroedinger equations, which are ubiquitous equations in nonlinear optics, are predominantly unstable and the underlying mathematical mechanism will be explained.