  The dual dynamics of Einstein gravity on AdS$_3$ supplemented with boundary
conditions of KdV-type is identified. It corresponds to a two-dimensional field
theory at the boundary, described by a novel action principle whose field
equations are given by two copies of the "potential modified KdV equation". The
asymptotic symmetries then transmute into the global Noether symmetries of the
dual action, giving rise to an infinite set of commuting conserved charges,
implying the integrability of the system. Noteworthy, the theory at the
boundary is non-relativistic and possesses anisotropic scaling of Lifshitz
type.
