Multisolitons for the defocusing energy critical wave equation with potentials (Q1799451)

The paper addresses a three-dimensional nonlinear equation if the D'Alembert type. It includes a self-repulsive quintic nonlinear term and several localized potential terms, moving at different velocities: \[ \partial_{tt}u - \Delta u +\sum_{j=1}^mV_J(x-v_jt)u + u^5 = 0, \] where the trapping potential decays at $|x|\to \infty$ as $(1 + |x|)^{-\beta}$. The paper presents a proof of the existence of solutions in the form of a set of solitons pinned to individual movig trapping potentials, and a proof of their stability in the energy space. Collisions between the moving solitons are considered too.