  The aim of this paper is two fold. We show that if a complex function $F$ on
$\C$ operates in the modulation spaces $M^{p,1}(\R^n)$ by composition, then $F$
is real analytic on $\R^2 \approx \C$. This answers negatively, the open
question posed in [M. Ruzhansky, M. Sugimoto, B. Wang, Modulation Spaces and
Nonlinear Evolution Equations, arXiv:1203.4651], regarding the general power
type nonlinearity of the form $|u|^\alpha u$. We also characterise the
functions that operate in the modulation space $M^{1,1}(\R^n)$.
  The local well-posedness of the NLS, NLW and NLKG equations for the `real
entire' nonlinearities are also studied in some weighted modulation spaces
$M^{p,q}_s(\R^n)$.
