Unitarily-invariant integrable systems and geometric curve flows in SU (n+1)/U(n) and SO(2n)/U(n)

作者：Ahmed Ahmed^*; Anco Stephen C; Asadi Esmaeel

来源：Journal of Physics A-Mathematical and Theoretical, 2018, 51(6): 065205.

DOI：10.1088/1751-8121/aaa193

• integrable system
• curve flow
• symmetric space

Bi-Hamiltonian hierarchies of soliton equations are derived from geometric non-stretching (inelastic) curve flows in the Hermitian symmetric spaces SU(n + 1)/U(n) and SO(2n)/U( n). The derivation uses Hasimoto variables defined by a moving parallel frame along the curves. As main results, new integrable multi-component versions of the Sine-Gordon (SG) equation and the modified Korteveg-de Vries (mKdV) equation, as well as a novel nonlocal multi-component version of the nonlinear Schrodinger (NLS) equation are obtained, along with their bi-Hamiltonian structures and recursion operators. These integrable systems are unitarily invariant and correspond to geometric curve flows given by a non-stretching wave map and a mKdV analog of a non-stretching Schrodinger map in the case of the SG and mKdV systems, and a generalization of the vortex filament bi-normal equation in the case of the NLS systems.

• 出版日期2018-2-9