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 squareu + \u\(rho-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 = rho = 3 Our method is strong enough to deal with the subconformal power rho < 1 + 4/(n - 1). Thus we extend earlier results due to Baez Segal Zhou, Ginibre Velo and Strauss for this equation. © 2001 Elsevier Science.