Stabilization of Unsteady Nonlinear Waves by Phase-Space Manipulation

We introduce a dynamic stabilization scheme universally applicable to unidirectional nonlinear coherent waves. By abruptly changing the waveguiding properties, breathing of wave packets subject modulation instability can be stabilized as result abrupt expansion homoclinic orbit and its fall into an elliptic fixed point (center). apply this concept Schr\"odinger equation framework show that Akhmediev breather envelope, which is at core Fermi-Pasta-Ulam-Tsingou recurrence extreme events, frozen steady periodic (dnoidal) by suitable variation single external physical parameter. experimentally demonstrate general approach in particular case surface gravity water waves propagating flume with bathymetry change. Our results highlight influence topography waveguide properties on lifetime confirm possibility control them.