Abstract: A system of equations combining the 1D Schrödinger equation and the point vortex system has been derived by Klein, Majda and Damodaran to modelize the evolution of nearly parallel vortex filaments in 3D incompressible fluids. In this talk I will describe some dynamics for this system such as travelling waves, collisions and finite-time blow-up. I will finally present the case of pairs of filaments. This is joint work with Valeria Banica and Erwan Faou.