NUMERICAL CHAOS, ROUNDOFF ERRORS, AND HOMOCLINIC MANIFOLDS

The focusing nonlinear Schrodinger equation is numerically integrated over moderate to long time intervals. In certain parameter regimes sma ll errors on the order of roundoff grow rapidly and saturate at values comparable to the main wave. Although the constants of motion are nea rly preserved, a serious phase instability (chaos) develops in the num erical solutions. The instability is found to be associated with homoc linic structures and the underlying mechanisms apply equally well to m any Hamiltonian wave systems.