Hasimoto variables, generalized vortex filament equations, Heisenberg models and Schrödinger maps arising from group-invariant NLS systems

Abstract

The deep geometrical relationships holding among the NLS equation, the vortex filament equation, the Heisenberg spin model, and the Schrödinger map equation are extended to the general setting of Hermitian symmetric spaces. New results are obtained by utilizing a generalized Hasimoto variable which arises from applying the general theory of parallel moving frames. The example of complex projective space ℂPN=SU(N+1)∕U(N) is used to illustrate the method and results.