Modulation instability in higher-order nonlinear Schrödinger equations

We investigate the dynamics of modulation instability (MI) and the corresponding breather solutions to the extended nonlinear Schrödinger equation that describes the full scale growth-decay cycle of MI. As an example, we study modulation instability in connection with the fourth-order equation in detail. The higher-order equations have free parameters that can be used to control the growth-decay cycle of the MI; that is, the growth rate curves, the time of evolution, the maximal amplitude, and the spectral content of the Akhmediev Breather strongly depend on these coefficients.Published versionN.A. and A.A. acknowledge the support of the Australian Research Council (Discovery Project Nos. DP140100265 and DP150102057)