In this article, we will show the scattering of the cubic defocusing nonlinear Schrödinger equation on the waveguide R2 ×T in H1. We first establish the linear profile decomposition in H1(R2 ×T) motivated by the linear profile decomposition of the mass-critical Schrödinger equation in L2(R2). Then by using the solution of the cubic resonant nonlinear Schrödinger system to approximate the nonlinear profile, we can prove scattering in H1 by using the concentration-compactness/rigidity method.
- Nonlinear Schrödinger equation
- Profile decomposition