  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.
