Loss of stability of a solitary wave through exciting a cnoidal wave on a Fermi-Pasta-Ulam ring

TL;DR

This study investigates how a solitary wave on a Fermi-Pasta-Ulam ring interacts with a cnoidal wave, leading to the eventual destabilization of the solitary wave through energy exchange and phonon radiation.

Contribution

It reveals the mechanism of solitary wave destabilization caused by excitation and interaction with cnoidal waves in a nonlinear lattice system.

Findings

Cnoidal waves can coexist with solitary waves for extended periods.

Energy exchange between waves causes oscillations in nonlinearity indicators.

Interaction with phonons ultimately destroys the solitary wave.

Abstract

The spatiotemporal propagation behavior of a solitary wave is investigated on a Fermi-Pasta-Ulam ring. We observe the emergence of a cnoidal wave excited by the solitary wave. The cnoidal wave may coexist with the solitary wave for a long time associated with the periodic exchange of energy between these two nonlinear waves. The module of the cnoidal wave, which is considered as an indicator of the nonlinearity, is found to oscillate with the same period of the energy exchange. After the stage of coexistence, the interaction between these two nonlinear waves leads to the destruction of the cnoidal wave by the radiation of phonons. Finally, the interaction of the solitary wave with phonons leads to the loss of stability of the solitary wave.