Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schrödinger equation

We prove that the non-radial sign-changing solutions to the nonlinear Schrodinger equation ∆u− u + |u|p−1u = 0 in R , u ∈ H(R ) constructed by Musso, Pacard and Wei [19] is non-degenerate. This provides the first example of non-degenerate sign-changing solution with finite energy to the above nonlinear Schrodinger equation.