Analytic study of a coupled Kerr-SBS system

TL;DR

This paper analytically investigates a coupled Kerr-SBS system using singularity structure analysis and symmetry methods, concluding that closed-form solutions are unlikely and proving the nonexistence of traveling wave solutions.

Contribution

It provides a detailed analytic study of the coupled Kerr-SBS PDE system, exploring singularities and symmetries to understand solution structures and limitations.

Findings

Singularity structure too complex for closed-form solutions

Proof of nonexistence of traveling wave solutions

Symmetry analysis used to reduce system complexity

Abstract

In order to describe the coupling between the Kerr nonlinearity and the stimulated Brillouin scattering, Mauger et alii recently proposed a system of partial differential equations in three complex amplitudes. We perform here its analytic study by two methods. The first method is to investigate the structure of singularities, in order to possibly find closed form singlevalued solutions obeying this structure. The second method is to look at the infinitesimal symmetries of the system in order to build reductions to a lesser number of independent variables. Our overall conclusion is that the structure of singularities is too intricate to obtain closed form solutions by the usual methods. One of our results is the proof of the nonexistence of traveling waves.