Abstract
It is well-known that third-order dispersion (TOD) plays no role in the onset of modulation instability in the nonlinear Schrödinger (NLS) family of systems. Here we demonstrate that the characteristics of modulational instability can be dramatically altered by the TOD in two different nonlinear systems, namely Wannier exciton mass in a ZnCdSe/ZnSe semiconductor superlattice and nonlinear pulse/beam propagation in a Kerr-like waveguide under non-slowly varying envelope approximation (non-SVEA), with spatial dispersion. Further we reveal the results of numerical simulations suggesting the existence of recently much studied Akhmediev-type breathers and Peregrine-like rogue waves due to the nonlinear development of MI stemming from the TOD.
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