Gamow Vectors Explain the Shock "Batman" Profile

TL;DR

This paper introduces a novel method using Gamow vectors of a reversed harmonic oscillator to analytically describe dispersive shock waves and undular bores in nonlinear media, confirmed by experiments.

Contribution

It presents a new analytical approach based on Gamow vectors for understanding shock wave dynamics beyond traditional methods.

Findings

Theoretical predictions match experimental observations of undulation periods.

Quantized decay patterns of Gamow vectors are observed experimentally.

Gamow vectors effectively describe extreme nonlinear phenomena.

Abstract

The description of shock waves beyond the shock point is a challenge in nonlinear physics. Finding solutions to the global dynamics of dispersive shock waves is not always possible due to the lack of integrability. Here we propose a new method based on the eigenstates (Gamow vectors) of a reversed harmonic oscillator in a rigged Hilbert space. These vectors allow analytical formulation for the development of undular bores of shock waves in a nonlinear nonlocal medium. Experiments by a photothermal induced nonlinearity confirm theoretical predictions: as the undulation period as a function of power and the characteristic quantized decays of Gamow vectors. Our results demonstrate that Gamow vector are a novel and effective paradigm for describing extreme nonlinear phenomena.