# Multisolitons for the defocusing energy critical wave equation with potentials

## TL;DR

This paper constructs and analyzes multisoliton solutions for the defocusing energy critical wave equation with potentials, demonstrating their asymptotic stability despite strong interactions due to slow decay rates.

## Contribution

It develops new reversed Strichartz estimates for wave equations with charge transfer Hamiltonians and proves the stability of multisoliton solutions in this setting.

## Key findings

- Constructed multisoliton solutions with both stable and unstable solitons.
- Proved asymptotic stability of these multisoliton solutions.
- Established reversed Strichartz and local decay estimates for the charge transfer model.

## Abstract

We construct multisoliton solutions to the defocusing energy critical wave equation with potentials in $\mathbb{R}^{3}$ based on regular and reversed Strichartz estimates developed in \cite{GC3} for wave equations with charge transfer Hamiltonians. We also show the asymptotic stability of multisoliton solutions. The multisoliton structures with both stable and unstable solitons are covered. Since each soliton decays slowly with rate $\frac{1}{\left\langle x\right\rangle }$, the interactions among the solitons are strong. Some reversed Strichartz estimates and local decay estimates for the charge transfer model are established to handle strong interactions.