  It is well-known that third-order dispersion (TOD) never allows the
continuous wave of any nonlinear Schroedinger (NLS) type system to experience
modulational instability (MI). Remarkably, we demonstrate a new kind of MI
induced by TOD with spatial dispersion accounting for Wannier exciton mass in a
ZnCdSe/ZnSe semiconductor superlattice. We also numerically predict the
existence of novel Akhmediev breathers and Peregrine solitons due to the
nonlinear development of MI with TOD.
