Extreme spectral asymmetry of Akhmediev breathers and Fermi-Pasta-Ulam recurrence in a Manakov system

The dynamics of Fermi-Pasta-Ulam (FPU) recurrence in a Manakov system is studied analytically. Exact Akhmediev breather (AB) solutions for this system are found that cannot be reduced to the ABs of a single-component nonlinear Schr\"odinger equation. Expansion-contraction cycle of the corresponding spectra with an infinite number of sidebands is calculated analytically using a residue theorem. A distinctive feature of these spectra is the asymmetry between positive and negative spectral modes. A practically important consequence of the spectral asymmetry is a nearly complete energy transfer from the central mode to one of the lowest-order (left or right) sidebands. Numerical simulations started with modulation instability of plane waves confirm the findings based on the exact solutions. It is also shown that the full growth-decay cycle of the AB leads to the nonlinear phase shift between the initial and final states in both components of the Manakov system. This finding shows that the final state of the FPU recurrence described by the vector ABs is not quite the same as the initial state. Our results are applicable and can be observed in a wide range of two-component physical systems such as two-component waves in optical fibers, two-directional waves in crossing seas, and two-component Bose-Einstein condensates.