HOMOCLINIC MANIFOLDS AND NUMERICAL CHAOS IN THE NONLINEAR SCHRODINGER-EQUATION

Crossings of homoclinic manifolds is a well known mechanism underlying observed;chaos in low dimensional systems. We discuss an analogous si tuation as it pertains to the numerical simulation of a well known int egrable partial differential equation, the nonlinear Schrodinger equat ion. In various parameter regimes, depending on the initial data, nume rical chaos is observed due to either truncation effects or errors on the order of roundoff. The explanation of the underlying cause of the chaos being due to crossing of homoclinic manifolds induced by the num erical errors is elucidated. The nonlinear Schrodinger equation is pro totypical of a much wider class of nonlinear systems in which computat ional chaos can be a significant factor.