A new U(1)-invariant nonlocal coupled nonlinear Schrödinger type system consists of a real scalar and two different complex variables as well as its equivalent imaginary quaternionic–complex version is obtained from geometric non-stretching curve flows in the quaternionic–Kähler symmetric space G2/SO(4). The derivation uses Hasimoto variables imposed by a parallel moving frame along the curve. The pseudo-differential bi-Hamiltonian and recursion operators as well as geometric curve evolution from soldering relations of the corresponding curvature and torsion are explicitly computed. The Lax pair for the system is derived by revisiting Drinfeld–Sokolov construction.

中文翻译：

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G2/SO(4) 中几何非拉伸曲线流的非局部 U(1)-不变非线性薛定谔系统

一个新的ü(1)-不变的非局部耦合非线性薛定谔型系统由一个实标量和两个不同的复变量组成，它的等效虚四元复数版本是从四元数-Kähler 对称空间中的几何非拉伸曲线流获得的G2/小号○(4). 推导使用由沿曲线的平行移动框架施加的 Hasimoto 变量。显式计算了伪微分双哈密顿算子和递归算子以及相应曲率和扭转的焊接关系的几何曲线演化。系统的 Lax 对是通过重新审视 Drinfeld-Sokolov 构造推导出来的。