Sasa-Satsuma equation, unstable plane waves and heteroclinic connections

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.