Existence of purely attractive interaction regimes for cavity soliton pairs

Determine whether any parameter regime of the normalized Lugiato–Lefever equation for pumped Kerr resonators yields a purely attractive asymptotic interaction between two well-separated cavity solitons, i.e., a soliton-pair drift velocity that remains strictly negative across the large-separation regime, as opposed to the purely repulsive (monotone-tail) or alternating attraction–repulsion (oscillatory-tail) behaviors identified in this work.

Background

The paper derives asymptotically exact equations of motion for the separation of two cavity solitons governed by the Lugiato–Lefever equation. It shows that when soliton tails decay monotonically, the effective interaction is purely repulsive and decreases exponentially with separation, while oscillatory tails lead to an interaction that alternates between attraction and repulsion with exponentially decreasing amplitude.

In all studied cases, the authors observed either purely repulsive interactions (monotone tails) or oscillatory interactions with alternating sign. They did not observe any parameter regime that produces purely attractive interactions, but they explicitly state that they cannot rule out this possibility, leaving open the question of whether such regimes exist.