  It is shown that the Ablowitz-Kaup-Newell-Segur (AKNS) integrable hierarchy
can be obtained as the dynamical equations of three-dimensional General
Relativity with a negative cosmological constant. This geometrization of AKNS
system is possible through the construction of novel boundary conditions for
the gravitational field. These are invariant under an asymptotic symmetry group
characterized by an infinite set of AKNS commuting conserved charges.
Gravitational configurations are studied by means of $SL(2,\mathbb{R})$
conjugacy classes. Conical singularities and black hole solutions are included
in the boundary conditions.
