Periodic solution of the time-space fractional Sasa-Satsuma equation in the monomode optical fibers by the energy balance theory

Abstract

Abstract Zhang and Wang developed the periodic solution of the time-space fractional Sasa-Satsuma equation by an ancient Chinese algorithm in EPL, 137 (2022) 62001. In this letter, a new method called the energy balance theory (EBT) is used to study the problem. This theory offers a promising approach by constructing the variational principle and the Hamiltonian for the problem. As anticipated, the solution obtained by the EBT is the same as the solution obtained in the above-mentioned EPL paper, which strongly verifies the effectiveness and reliability of the EBT. Finally, graphical simulations of the solution with different fractional orders are presented in the form of 2-D and 3-D surfaces. The discovery of this work is expected to contribute to the study of periodic solutions of the partial differential equations arising in optics.