Existence of multi-solitons with any parameters for the 5D energy critical wave equation
Analysis of PDEs
2025-10-23 v1
Abstract
For the focusing, energy critical wave equation in dimension 5, we construct multi-solitons with any number of solitons, any choice of signs, speeds, scaling parameters and translation parameters. This requires to revisit in depth previous constructions of multi-solitons based on a unidirectional approach, to fully take into account the dimension of the space and the possibility for solitons to move in any direction. Then, as a consequence of this more general construction and of the arguments developed in a previous article, the inelastic nature of any collision of solitons is proved under a non-cancellation assumption on the parameters.
Keywords
Cite
@article{arxiv.2510.19609,
title = {Existence of multi-solitons with any parameters for the 5D energy critical wave equation},
author = {Yvan Martel and Frank Merle},
journal= {arXiv preprint arXiv:2510.19609},
year = {2025}
}