Existence of multi-solitons with any parameters for the 5D energy critical wave equation

TL;DR

This paper constructs multi-solitons with arbitrary parameters for the 5D energy critical wave equation, extending previous methods to higher dimensions and multiple directions, and proves inelastic collisions under certain conditions.

Contribution

It introduces a comprehensive construction of multi-solitons with any parameters for the 5D wave equation, accounting for multidirectional movement and general configurations.

Findings

Multi-solitons exist with any parameters in 5D energy critical wave equation.

The construction accounts for solitons moving in any direction.

Inelastic collision behavior is established under non-cancellation conditions.

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.