This work demonstrates the existence of multisoliton solutions in three-dimensional systems, suggesting new dynamics in gravitational interactions.
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-Raphaël [Comm. Pure Appl. Math. 62 (2009), pp. 1501–1550] on two-soliton solutions.
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Yutong Wu (2026) studied this question.
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