[HTML][HTML] Hasimoto variables, generalized vortex filament equations, Heisenberg models and Schrödinger maps arising from group-invariant NLS systems
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 ℂ PN= SU (N+ 1)∕ U (N) is used
to illustrate the method and results.
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 ℂ PN= SU (N+ 1)∕ U (N) is used
to illustrate the method and results.
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 ℂ P N= S U (N+ 1)∕ U (N) is used to illustrate the method and results.
Elsevier
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