Instabilities are common phenomena frequently observed in nature, sometimes leading to unexpected
catastrophes and disasters in seemingly normal conditions. One prominent 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 leads to a
growth-decay cycle of unstable waves and is therefore related to Fermi-Pasta-Ulam (FPU) recurrence
since breather solutions of the nonlinear Schrödinger 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 efect 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.