Scattering Problem for the Nonlinear Wave Equation in the Finite Energy and Conformal Charge Space

The theory of scattering is studied for the nonlinear wave equation □u+|u|ρ−1 u=0 in space dimensions n=3, 4. We give a new proof of the asymptotic completeness in the finite energy and conformal charge space for n=ρ=3. Our method is strong enough to deal with the subconformal power ρ<1+4/(n−1). Thus we extend earlier results due to Baez–Segal–Zhou, Ginibre–Velo and Strauss for this equation.