  Instabilities are common phenomena frequently observed in nature, sometimes
leading to unexpected catastrophes and disasters in seemingly normal
conditions. The simplest form of instability in a distributed system is its
response to a harmonic modulation. Such instability has special names in
various branches of physics and is generally known as modulation instability
(MI). The MI is tightly related to Fermi-Pasta-Ulam (FPU) recurrence since
breather solutions of the nonlinear Schr\"odinger equation (NLSE) are known to
accurately describe growth and decay of modulationally unstable waves in
conservative systems. Here, we report theoretical, numerical and experimental
evidence of the effect of dissipation on FPU cycles in a super wave tank,
namely their shift in a determined order. In showing that ideal NLSE breather
solutions can describe such dissipative nonlinear dynamics, our results may
impact the interpretation of a wide range of new physics scenarios.
