Higher-order modulation instability and multi-Akhmediev breathers of Manakov equations: Frequency jumps over the stable gaps between the instability bands

We study higher-order modulation instability phenomena in the frame of Manakov equations. Evolution that starts with a single pair of sidebands expands over several higher harmonics. The choice of initial pair of sidebands influences the structure of unstable frequency components and changes drastically the wave evolution, leading, in some cases, to jumps across spectral components within the discrete spectrum. This complex dynamics includes several growth-decay cycles of evolution. We show this using numerical simulations of the modulation instability process and confirm the results using the exact multi-Akhmediev breather solutions. Detailed explanations of the observed phenomena are given.