Modulation Instability and Phase-Shifted Fermi-Pasta-Ulam Recurrence

TL;DR

This paper investigates how dissipation affects Fermi-Pasta-Ulam recurrence cycles in nonlinear systems, combining theory, simulations, and experiments to reveal phase shifts caused by dissipation.

Contribution

It demonstrates that ideal NLSE breather solutions can describe dissipative nonlinear dynamics, revealing phase shifts in FPU recurrence cycles due to dissipation.

Findings

Dissipation causes a phase shift in FPU recurrence cycles.

Theoretical, numerical, and experimental evidence supports the findings.

Dissipative effects can be modeled using NLSE breather solutions.

Abstract

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.