Soliton resolution for the radial critical wave equation in all odd space dimensions

Consider the energy-critical focusing wave equation in odd space dimension $N\geq 3$. The 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 energy norm of behaves asymptotically as sum modulated $W$s, decoupled by scaling, radiation term. The proof essentially boils down fact does not have purely nonradiative multisoliton solutions. overcomes fundamental obstruction for extension 3D case (treated our previous work, Cambridge Journal Mathematics 2013, arXiv:1204.0031) reducing study finite dimensional system ordinary differential equations on modulation parameters. key ingredient show creates some radiation, contradicting existence pure multisolitons.