Abstract
A new [Formula: see text]-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 [Formula: see text]. 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.
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