Hamiltonian Integrability of Two-Component Short Pulse Equations

TL;DR

This paper establishes the bi-Hamiltonian structure for certain two-component short pulse equations, advancing the understanding of their integrability properties in anisotropic media.

Contribution

It introduces the bi-Hamiltonian framework for two-component short pulse equations, a novel step in analyzing their integrability.

Findings

Bi-Hamiltonian structure identified for specific equations

Enhanced understanding of integrability in anisotropic media

Generalization of the short pulse equation

Abstract

We obtain the bi-Hamiltonian structure for some of the two-component short pulse equations proposed in the literature to generalize the original short pulse equation when polarized pulses propagate in anisotropic media.