Construction of Quasi-periodic solutions with the same Gevrey index as nonlinear terms in Multi-Dimensional NLS

We investigate the persistency of quasi-periodic solutions to multi-dimensional nonlinear Schrödinger equations (NLS) involving Gevrey smooth nonlinearity with an arbitrary Gevrey index $\alpha >1$. By applying the Craig-Wayne-Bourgain (CWB) method, we establish the existence of quasi-periodic solutions that are Gevrey smooth with the same Gevrey index as the nonlinearity.