Normal Modes of the Small-Amplitude Oscillon

TL;DR

This paper investigates the normal modes of small-amplitude oscillons in (1+1) dimensions, deriving eigenvectors of the monodromy matrix to understand their periodic perturbations and implications for quantization.

Contribution

It explicitly finds the eigenvectors of the monodromy matrix for small-amplitude oscillons, providing a foundation for quantization approaches similar to sine-Gordon breathers.

Findings

Eigenvectors of the monodromy matrix are explicitly derived.

Small amplitude oscillons are shown not to reflect small amplitude radiation.

Results are model-independent, applicable to various oscillon configurations.

Abstract

Consider a classical (1+1)-dimensional oscillon of small amplitude $\epsilon$. To all orders in $\epsilon$, the oscillon solution is exactly periodic. We study small perturbations of such periodic configurations. These perturbations are themselves periodic up to a monodromy matrix. We explicitly find the eigenvectors of the monodromy matrix, which are the analogues of normal modes for oscillons. Dashen, Hasslacher and Neveu used such eigenvectors to quantize the sine-Gordon breather, and we suspect that they will be necessary to quantize the oscillon. Our results, regardless of the chosen model, suggest that low amplitude oscillons do not reflect small amplitude radiation.