Abstract
We construct K-solitons of the focusing energy-critical nonlinear wave equation in five-dimensional space, i.e. solutions u of the equation such that where and for any , Wk is the Lorentz transform of the explicit standing soliton , with any speed , satisfying for , and an explicit smallness condition. The proof extends the refined method of construction of asymptotic multi-solitons from Martel and Merle (2016 Arch. Ration. Mech. Anal. 222 1113–60; Martel and Merle 2018 Inventiones Math. 214 1267–363).
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