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For the focusing energy critical wave equation in 5D, we construct a solutionshowing the inelastic nature of the collision of any two solitons, except thespecial case of two solitons of same scaling and opposite signs. Beyond its owninterest as one of the first rigorous studies of the collision of solitons fora non-integrable model, the case of the quartic gKdV equation being partiallytreated by the authors in previous works, this result can be seen as part of awider program aiming at establishing the soliton resolution conjecture for thecritical wave equation. This conjecture has already been established in the 3Dradial case and in the general case in 3, 4 and 5D along a sequence of times byDuyckaerts, Kenig and Merle. The study of the nature of the collision requiresa refined approximate solution of the two-soliton problem and a precisedetermination of its space asymptotics. To prove inelasticity, theseasymptotics are combined with the method of channels of energy.

Inelasticity of soliton collisions for the 5D energy critical wave equation