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Integrability in three-dimensional gravity: eigenfunction-forced KdV flows
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DOI：10.1007/jhep07(2026)120.png)
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Abstract
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We uncover a direct connection between three-dimensional gravity with chiral boundary conditions and a class of forced integrable systems. Starting from the Chern-Simons formulation, we derive consistent boundary conditions on a non-compact spatial slice, leading to boundary dynamics described by the potential modified KdV hierarchy. The dynamics reduce to a forced KdV equation, where the forcing term is determined self-consistently by the eigenfunctions of the associated Schrödinger operator. Using the inverse scattering transform, the reflectionless sector is solved via the Gelfand-Levitan-Marchenko method, while the radiative sector exhibits universal dispersive decay. This framework unifies AdS3 boundary dynamics with integrable hierarchies and elucidates the roles of solitons and radiation in the dual conformal field theory.
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