  In this paper, we consider a constrained maximization problem related to
planar vortex pairs with prescribed impulse. We prove existence, stability and
asymptotic behavior for the maximizers, hence obtain a family of stable
traveling vortex pairs approaching a pair of point vortices with equal
magnitude and opposite signs. As a corollary, we get fine asymptotic estimates
for Burton's vortex pairs with large impulse. For the non-concentrated case, we
prove a form of stability for the Chaplygin-Lamb dipole.
