Existence of multisoliton solutions of the gravitational Hartree equation in three dimensions

TL;DR

This paper proves the existence of multisoliton solutions for the 3D gravitational Hartree equation, demonstrating complex multi-body dynamics and extending previous two-soliton results.

Contribution

It introduces new multisoliton solutions in three dimensions, generalizing prior work on two-soliton solutions and capturing diverse dynamical behaviors.

Findings

Existence of multisoliton solutions with various trajectories.

Generalization of previous two-soliton results.

Enhanced understanding of multi-body gravitational interactions.

Abstract

We prove the existence of multisoliton solutions of the three-dimensional gravitational Hartree equation whose trajectories follow many body dynamics of hyperbolic, parabolic or hyperbolic-parabolic types. This work generalizes and improves the result of Krieger-Martel-Rapha\"el on two-soliton solutions.