The (2+1) sine-Gordon Equation and Dynamics of Localized Pulses
Monday, October 25, 2004 - 1:30pm - 2:20pm
Jack Xin (The University of Texas at Austin)
The (2+1) sine-Gordon (SG) equation is derived from a Maxwell-Bloch system to model the dynamics of localized light pulses in two space dimensional cubic nonlinear materials. A class of nonlinear Schroedinger equations with both focusing and defocusing mechanisms appears as underlying asymptotic description for both the propagation and interaction phenomena.The dynamical persistence of pulses is related to the internal oscillations. Alternative asymptotic methods are reviewed to shed more light. Numerical simulations show the robustness of solitary wave like interaction on the plane.