Construction of multi-solitons for the energy-critical wave equation in dimension 5

Abstract

We construct 2-solitons of any speed of the focusing energy-critical nonlinear wave equation in dimension 5. The existence result also holds for the case of K-solitons, for any K >2, assuming that the speeds are collinear. The main difficulty of the construction is the strong interaction between the solitons due to the slow spatial decay of the single soliton. This is in contrast with previous constructions of multi-solitons for other nonlinear models (like generalized KdV and nonlinear Schrodinger equations in energy subcritical cases), where the interactions are exponentially small in time due to the exponential decay of the solitons.