Investigation of the periodic solution of the time-space fractional Sasa-Satsuma equation arising in the monomode optical fibers

School of Physics and Electronic Information Engineering, Henan Polytechnic University - Jiaozuo, 454003, China

^(a) plzhang@hpu.edu.cn (corresponding author)

Received: 25 June 2021
Accepted: 27 September 2021

Abstract

In this paper, the time-space fractional Sasa-Satsuma equation is considered. A novel and interesting method called as He's frequency formulation, which is derived from the ancient Chinese algorithm (ACG) Ying Bu Zu Shu, is employed to construct its periodic solution. This ancient algorithm originated from an ancient Chinese mathematics monograph —The Nine Chapters on the Mathematical Art— compiled in the Han Dynasty about the second century AD. As anticipated, the obtained solution is consistent with that of the variational method. It strongly verifies the effectiveness and reliability of the proposed method. Finally, the performances of the solution with different fractional orders are presented through the 2D and 3D surfaces. The discovery of this work is expected to contribute to the study of periodic solutions in physics.