The Fukumoto-Moffattʼs model in the vortex filament and generalized bi-Schrödinger maps

► We introduce the concept of generalized bi-Schrödinger maps. ► The Fukumoto-Moffattʼs model is proved to be just such maps from R1 into S2. ► This gives a geometric interpretation of the Fukumoto-Moffattʼs model.