Energy exchange and transition to localization in the asymmetric Fermi-Pasta-Ulam oscilliatory chain

TL;DR

This paper investigates energy exchange and localization in asymmetric FPU chains, demonstrating that resonant interactions of nonlinear normal modes can lead to energy transfer and localization, supported by analytical and numerical methods.

Contribution

It extends the understanding of energy exchange mechanisms to realistic asymmetric chains and introduces analytical descriptions based on effective particles and Limiting Phase Trajectories.

Findings

Resonant interactions cause energy exchange and localization.

Analytical models match numerical simulations.

Linearization of equations of motion is possible.

Abstract

A finite (periodic) FPU chain is chosen as a convenient point for investigating the energy exchange phenomenon in nonlinear oscillatory systems. As we have recently shown, this phenomenon may occur as a consequence of the resonant interaction between high-frequency nonlinear normal modes. This interaction determines both the complete energy exchange between different parts of the chain and the transition to energy localization in an excited group of particles. In the paper, we demonstrate that this mechanism can exist in realistic (asymmetric) models of atomic or molecular oscillatory chains. Also, we study the resonant interaction of conjugated nonlinear normal modes and prove a possibility of linearization of the equations of motion. The theoretical constructions developed in this paper are based on the concepts of "effective particles" and Limiting Phase Trajectories. In particular, an analytical description of energy exchange between the "effective particles" in the terms of non-smooth functions is presented. The analytical results are confirmed with numerical simulations.