Deterministic Chaos vs Integrable Models

TL;DR

This paper demonstrates that certain classical integrable models, like KdV and sine-Gordon, can display features typical of chaos due to the inverse scattering map, challenging traditional distinctions.

Contribution

It reveals that integrable models can exhibit chaotic-like features because of the inverse scattering map, supported by analytical, numerical, and general arguments.

Findings

Integrable models show chaos-like features under small deformations.

Inverse scattering map influences the emergence of chaos features.

Evidence from KdV and sine-Gordon models supports the findings.

Abstract

In this work we present analytical and numerical evidences that classical integrable models possessing infinitely many degrees of freedom unexpectedly exhibit some features that are typical of chaotic systems. By studying how the conserved charges change under a small deformation of the initial conditions, we conclude that the inverse scattering map is responsible for the presence of these features, in spite of the system being integrable. We investigate this phenomenon in the explicit examples of the KdV equation and the sine-Gordon model and further provide general arguments supporting this statement.