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The spectra of rogue waves of Manakov equations that exist in both focusing or defocusing regimes are derived in analytic form. These spectra are asymmetric during their whole expansion-contraction cycle. They have triangular shape at each side of the spectrum in the log scale. Such spectra are characterised by two quantities: the slopes of the spectra and the spectral jump at zero frequency. We confirm our analytical results using numerical simulations., Comment: 10 pages, 5 figures

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 MI process and confirm the results using the exact multi-Akhmediev breather solutions. Detailed explanation of the observed phenomena are given., Comment: 9 pages, 6 figures

We developed an exact theory of the super-regular (SR) breathers of Manakov equations. We have shown that the vector SR breathers do exist both in the cases of focusing and defocusing Manakov systems. The theory is based on the eigenvalue analysis and on finding the exact links between the SR breathers and modulation instability. We have shown that in the focusing case the localised periodic initial modulation of the plane wave may excite both a single SR breather and the second-order SR breathers involving four fundamental breathers., Comment: 6 pages, 3 figures

We reveal a new class of \textit{non-degenerate} Akhmediev breather (AB) solutions of Manakov equations that only exist in the focusing case. Based on exact solutions, we present the existence diagram of such excitations on the frequency-wavenumber plane. Conventional single-frequency modulation instability leads to simultaneous excitation of three ABs with two of them being non-degenerate., Comment: 6 pages, 3 figures

We study the dynamics of Kuznetsov-Ma solitons (KMS) in the framework of vector nonlinear Schr\"odinger (Manakov) equations. Exact multi-parameter family of solutions for such KMSs is derived. This family of solutions includes the known results as well as the previously unknown solutions in the form of the non-degenerate KMSs. We present the existence diagram of such KMSs that follows from the exact solutions. These non-degenerate KMSs are formed by nonlinear superposition of two fundamental KMSs that have the same propagation period but different eigenvalues. We present the amplitude profiles of new solutions, their exact physical spectra, their link to ordinary vector solitons and offer easy ways of their excitation using numerical simulations., Comment: 15 pages, 14 figures

In multi-component systems, several rogue waves can be simultaneously excited using simple initial conditions in the form of a plane wave with a small amplitude single-peak perturbation. This is in drastic contrast with the case of multi-rogue waves of a single nonlinear Schr\"{o}dinger equation (or other evolution equations) that require highly specific initial conditions to be used. This possibility arises due to the higher variety of rogue waves in multi-components systems each with individual eigenvalue of the inverse scattering technique. In theory, we expand the limited class of Peregrine-type solutions to a much larger family of non-degenerate rogue waves. The results of our work may explain the increased chances of appearance of rogue waves in crossing sea states (wind generated ocean gravity waves that form nonparallel wave systems along the water surface) as well as provide new possibilities of rogue wave observation in a wide range of multi-component physical systems such as multi-component Bose-Einstein condensates, multi-component plasmas and in birefringent optical fibres., Comment: 8pages,6figures