Craig W., Wayne C.E. Nonlinear Waves and the KAM Theorem: Nonlinear Degeneracies (50K, TeX) ABSTRACT. This paper describes how one can use ideas related to the Nash-Moser implicit function theorem to construct solutions of nonlinear wave equations of the form: $$ u_{tt} = u_{xx} - g(x,u) \qquad 0 < x < \pi,\; $$ We concentrate in this note on the case in which the nonlinear term $g(x,u)$, fails to satisfy a nondegeneracy condition which is the analogue of the twist condition in Moser twist mapping theorem.