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

¹ College of Science, China University of Petroleum - Beijing 102249, China
² Department of Mathematics and Physics, North China Electric Power University - Beijing 102206, China
³ Institute of Theoretical Physics, Shanxi University - Taiyuan, Shanxi 030006, China

^(a) xutao@cup.edu.cn (corresponding author)
^(b) micheller85@126.com (corresponding author)

Received: 28 November 2014
Accepted: 2 February 2015

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.