On integrability of the vector short pulse equation

TL;DR

This paper applies Painleve analysis to identify two new integrable cases of the vector short pulse equation, relevant for modeling polarized ultra-short light pulses in optical fibers.

Contribution

It introduces a novel application of Painleve analysis to find integrable cases of the vector short pulse equation, with implications for optical fiber technology.

Findings

Two new integrable cases identified via Painleve test.

Results applicable to polarized ultra-short light pulse propagation.

Enhanced understanding of the mathematical structure of the vector short pulse equation.

Abstract

Using the Painleve analysis preceded by appropriate transformations of nonlinear systems under investigation, we discover two new cases in which the Pietrzyk-Kanattsikov-Bandelow vector short pulse equation must be integrable due to the results of the Painleve test. Those cases are technologically important because they correspond to the propagation of polarized ultra-short light pulses in usual isotropic silica optical fibers.