Anti-dark and Mexican-hat solitons in the Sasa-Satsuma equation on the continuous wave background

TL;DR

This paper constructs new analytical anti-dark and Mexican-hat soliton solutions for the Sasa-Satsuma equation, revealing their unique interaction behaviors and stability properties on a continuous wave background in femtosecond pulse propagation.

Contribution

It introduces novel anti-dark and Mexican-hat soliton solutions for the Sasa-Satsuma equation using Darboux transformation, highlighting their interaction dynamics and stability features.

Findings

Anti-dark and Mexican-hat solitons can form on a CW background.

Solitons exhibit resonant, elastic, and inelastic interactions.

Energy exchange can convert one soliton type into another.

Abstract

In this letter, via the Darboux transformation method we construct new analytic soliton solutions for the Sasa-Satsuma equation which describes the femtosecond pulses propagation in a monomode fiber. We reveal that two different types of femtosecond solitons, i.e., the anti-dark (AD) and Mexican-hat (MH) solitons, can form on a continuous wave (CW) background, and numerically study their stability under small initial perturbations. Different from the common bright and dark solitons, the AD and MH solitons can exhibit both the resonant and elastic interactions, as well as various partially/completely inelastic interactions which are composed of such two fundamental interactions. In addition, we find that the energy exchange between some interacting soliton and the CW background may lead to one AD soliton changing into an MH one, or one MH soliton into an AD one.