On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau system

Abstract

> 0, we will concern its linearized operator L around the radially symmetric solution w(x) = (w + , w − ) : R 2 → C 2 of degree pair (1, 1) and prove the non-degeneracy result: the kernel of L is spanned by ∂w ∂x 1 , ∂w ∂x 2 in a natural Hilbert space. As an application of the non-degeneracy result, a solvability theory for the linearized operator L will be given.