  We demonstrate dynamical topological phase transitions in evolving
Su-Schrieffer-Heeger (SSH) lattices made of interacting soliton arrays, which
are entirely driven by nonlinearity and thereby exemplify emergent nonlinear
topological phenomena. The phase transitions occur from topologically
trivial-to-nontrivial phase in periodic succession with crossovers from
topologically nontrivial-to-trivial regime. The signature of phase transition
is gap-closing and re-opening point, where two extended states are pulled from
the bands into the gap to become localized topological edge states. Crossovers
occur via decoupling of the edge states from the bulk of the lattice.
