Soliton in a Well. Dynamics and Tunneling

TL;DR

This paper investigates the behavior of oscillating solitons in a well, deriving their radiation through tunneling using hydrodynamic methods with rigorous error control for finite times.

Contribution

It introduces a rigorous hydrodynamic approach to analyze soliton tunneling and radiation in a well, providing new insights into their dynamics.

Findings

Derived the leading order radiation formula for oscillating solitons.

Established rigorous error bounds for finite-time analysis.

Enhanced understanding of soliton tunneling mechanisms.

Abstract

We derive the leading order radiation through tunneling of an oscillating soliton in a well. We use the hydrodynamic formulation with a rigorous control of the errors for finite times.