Hasimoto variables, generalized vortex filament equations, Heisenberg models and Schrodinger 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 Schrodinger 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 CP^N= SU(N+1)/U(N) is used to illustrate the method and results.

arXiv comment48 pages. Published version

References in corpus (9)

• On the Differential Geometry of $G{L}_q(1|1)$
• Integrable generalizations of Schrodinger maps and Heisenberg spin models from Hamiltonian flows of curves and surfaces
• Conservation laws of scaling-invariant field equations
• Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces
• Hamiltonian Flows of Curves in symmetric spaces G/SO(N) and Vector Soliton Equations of mKdV and Sine-Gordon Type
• Symplectically-invariant soliton equations from non-stretching geometric curve flows
• Quaternionic Soliton Equations from Hamiltonian Curve Flows in HP^n
• Unitarily-invariant integrable systems and geometric curve flows in $SU(n+1)/U(n)$ and $SO(2n)/U(n)$
• Integrable Systems with Unitary Invariance from Non-stretching Geometric Curve Flows in the Hermitian Symmetric Space Sp(n)/U(n)

Cited by in corpus (1)

• Integrable spinor/quaternion generalizations of the nonlinear Schrodinger equation