Construction of excited multi-solitons for the 5D energy-critical wave equation

For the 5D energy-critical wave equation, we construct excited [Formula: see text]-solitons with collinear speeds, i.e. solutions text] of equation such that where for text], is Lorentz transform a non-degenerate and sufficiently decaying state, each different but speeds. The existence proof follows ideas Martel–Merle [Construction multi-solitons in dimension 5, Arch. Ration. Mech. Anal. 222(3) (2016) 1113–1160] Côte–Martel [Multi-travelling waves nonlinear Klein–Gordon Trans. Amer. Math. Soc. 370(10) (2018) 7461–7487] developed equations. In particular, rely on an energy method general coercivity property linearized operator.