  In this paper, we present two infinite-dimensional KAM theorems with
frequency-preserving for a nonresonant frequency of Diophantine type or even
weaker. To be more precise, under a nondegenerate condition for an
infinite-dimensional Hamiltonian system, we prove the persistence of a
full-dimensional KAM torus with the specified frequency independent of any
spectral asymptotics, by advantage of the generating function method. This
appears to be the first Kolmogorov type result in the infinite-dimensional
context. As a direct application, we provide a positive answer to Bourgain's
conjecture: full-dimensional invariant tori for 1D nonlinear Schr\"{o}dinger
equations do exist.
