Derive the emission spectrum from a driven soliton-horizon dynamics

Derive the analogue-Hawking emission spectrum from the dynamics of a driven soliton in a Raman-free Kerr medium, rather than imposing the thermal relation as an input of a kinematic model.

Background

The paper distinguishes results derived from the undriven generalized nonlinear Schrödinger equation from properties imposed by a kinematic horizon model. In particular, the thermal Bogoliubov relation and the associated entanglement are prescribed rather than obtained from a dynamical scattering calculation.

The discussion states that a fully driven stationary soliton-horizon solution and dynamical Hawking thermality are not demonstrated. The unresolved problem is therefore to formulate and analyze a driven, Raman-free Kerr model that produces the emission spectrum dynamically and establishes whether the analogue-Hawking interpretation follows from the underlying soliton dynamics.