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Non-radiative solutions of energy critical wave equations are such that theirenergy in an exterior region $|x|>R+|t|$ vanishes asymptotically in both timedirections. This notion, introduced by Duyckaerts, Kenig and Merle (J. Eur.Math. Soc., 2011), has been key in solving the soliton resolution conjecturefor these equations in the radial case. In the present paper, we first classifytheir asymptotic behaviour at infinity, showing that they correspond to a$k$-parameters family of solutions where $k$ depends on the dimension. Thisgeneralises the previous results (Duyckaerts, Kenig and Merle, Camb. J. Math.,2013 and Duyckaerts, Kenig, Martel and Merle, Comm. Math. Phys., 2022) in threeand four dimensions. We then establish a unique maximal extension of thesesolutions.

On classification of non-radiative solutions for various energy-critical wave equations