in this talk, we consider a vector valued nonlinear wave equation of the unknown $u(t, x) \in r^n$. suppose the energy density of the equation contains a nonlinear potential $v(u)/\epsilon^2$ which achieves its minimal value $0$ on a submanifold $m$ in $r^n$. as $\epsilon$ approaches $0$, i.e. as this potential approaches infinity, we are interested in the convergence of finite energy solutions. through a multi-scale formal asymptotic expansion involving rapid oscillations, j. keller and k. rubinstein (1991) found that the singular limits of those solutions satisfy a hyperboic pde system. we rigorously justified this convergence procedure and the local well-posedness of this system. in particular, when the initial data is well prepared, the limit system reduces to the wave map equation targeted on $m$. the comparison between the structures of the wave equation and the limit system and a more general picture of hamiltonian pdes with strong potentials, will also be briefly discussed.