Singularities and Global Solutions in the Schrodinger-Hartree Equation

Abstract

We present the random behaviour of the Schrödinger map equation, a geometric partial differential equation, by considering its evolution for regular polygonal curves in both Euclidean and hyperbolic spaces. The results obtained are consistent with those for the vortex filament equation, an equivalent form of the Schrödinger map equation in the Euclidean space, and thus, provide a novel extension to its usefulness as a pseudorandom number generator.