Rational W-shaped solitons on a continuous-wave background in the Sasa-Satsuma equation.

Abstract

We investigate the solution in rational form for the Sasa-Satsuma equation on a continuous background which describes a nonlinear fiber system with higher-order effects including the third-order dispersion, Kerr dispersion, and stimulated inelastic scattering. The W-shaped soliton in the system is obtained analytically. It is found that the height of hump for the soliton increases with decreasing the background frequency in certain parameter regime. The maximum height of the soliton can be three times the background's height and the corresponding profile is identical with the one for the well-known eye-shaped rogue wave with maximum peak. The numerical simulations indicate that the W-shaped soliton is stable with small perturbations. Particularly, we show that the W-shaped soliton corresponds to a stable supercontinuum pulse by performing exact spectrum analysis.