  In this paper we study quasiconcavity properties of solutions of Dirichlet
problems related to modified nonlinear Schr\"odinger equations of the type
$$-{\rm div}\big(a(u) \nabla u\big) + \frac{a'(u)}{2} |\nabla u|^2 = f(u) \quad
\hbox{in $\Omega$},$$ where $\Omega$ is a convex bounded domain of
$\mathbb{R}^N$. In particular, we search for a function $\varphi:\mathbb{R} \to
\mathbb{R}$, modeled on $f\in C^1$ and $a\in C^1$, which makes $\varphi(u)$
concave. Moreover, we discuss the optimality of the conditions assumed on the
source.
