  Consider the energy-critical focusing wave equation in odd space dimension
$N\geq 3$. The equation has a nonzero radial stationary solution $W$, which is
unique up to scaling and sign change. In this paper we prove that any radial,
bounded in the energy norm solution of the equation behaves asymptotically as a
sum of modulated $W$s, decoupled by the scaling, and a radiation term.
  The proof essentially boils down to the fact that the equation does not have
purely nonradiative multisoliton solutions. The proof overcomes the fundamental
obstruction for the extension of the 3D case (treated in our previous work,
Cambridge Journal of Mathematics 2013, arXiv:1204.0031) by reducing the study
of a multisoliton solution to a finite dimensional system of ordinary
differential equations on the modulation parameters. The key ingredient of the
proof is to show that this system of equations creates some radiation,
contradicting the existence of pure multisolitons.
