  We consider Calder\'{o}n's inverse boundary value problems for a class of
nonlinear Helmholtz Schr\"{o}dinger equations and Maxwell's equations in a
bounded domain in $\R^n$. The main method is the higher-order linearization of
the Dirichlet-to-Neumann map of the corresponding equations. The local
uniqueness of the linearized partial data Calder\'{o}n's inverse problem is
obtained following \cite{DKSU}. The Runge approximation properties and unique
continuation principle allow us to extend to global situations. Simultaneous
recovery of some unknown cavity$/$boundary and coefficients are given as some
applications.
