  We consider a branching-selection system in $\mathbb {R}$ with $N$ particles
which give birth independently at rate 1 and where after each birth the
leftmost particle is erased, keeping the number of particles constant. We show
that, as $N\to\infty$, the empirical measure process associated to the system
converges in distribution to a deterministic measure-valued process whose
densities solve a free boundary integro-differential equation. We also show
that this equation has a unique traveling wave solution traveling at speed $c$
or no such solution depending on whether $c\geq a$ or $c<a$, where $a$ is the
asymptotic speed of the branching random walk obtained by ignoring the removal
of the leftmost particles in our process. The traveling wave solutions
correspond to solutions of Wiener-Hopf equations.
