Science and Mathematics Faculty Publications

Sasa-Satsuma Equation, Unstable Plane Waves and Heteroclinic Connections (article)

Document Type

Article

Publication Date

7-2007

Journal Title

Chaos, Solitons & Fractals

Volume

33

Issue

2

First Page

374

Last Page

387

Abstract

The Sasa-Satsuma equation is an integrable perturbation of the nonlinear Schrödinger equation which models the effects of third-order dispersion, self-steepening and stimulated Raman scattering in the propagation of ultra-fast pulses in optical fiber transmission systems. The heteroclinic connections of the unstable plane waves are explicitly constructed using an auto-Bäcklund transformation obtained from inverse spectral theory. The modulus of the heteroclinic connection can have either a single peak or a double peak, depending on the amplitude of the unstable plane wave, even when only one unstable positive wavenumber is present.

Keywords

Sasa-Satsuma Equation

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