Modulation instability (MI) and Fermi-Pasta-Ulam (FPU) recurrence are central objects in physics. They can be considered as the origin of the nonlinear science. Rigorous analysis on full nonlinear evolution is only allowed for integrable system.  It is presently known as a family of exact periodic solutions.  A general result involving asymmetric dynamics in both time and frequency domains is given recently [PRL 2021,127.094102].