We address the dynamics of higher-order solitons in optical lattices, and
predict their self-splitting into the set of their single-soliton constituents.
The splitting is induced by the potential introduced by the lattice, together
with the imprinting of a phase tilt onto the initial multisoliton states. The
phenomenon allows the controllable generation of several coherent solitons
linked via their Zakharov-Shabat eigenvalues. Application of the scheme to the
generation of correlated matter waves in Bose-Einstein condensates is
discussed.Comment: 13 pages, 4 figures, to appear in Physical Review Letter
