Periodic solution of the time-space fractional complex nonlinear Fokas-Lenells equation by an ancient Chinese algorithm

As is known to all, the complex nonlinear Fokas-Lenells equation is widely used to describe the propagation of short pulses in optical fibers. In this work, we aim to study its time-space fractional modified form. An ancient Chinese algorithm called the Ying Bu Zu Shu(), which is from an ancient Chinese mathematics monograph-The Nine Chapters on the Mathematical Art() in about second century AD, is used to find its periodic solution. The solution obtained by our proposed method is the same as the one obtained via the variational method, which strongly proves the effectiveness and reliability of the proposed method. Finally, we plot the solution with different fractional orders in the form of 2-dimensional and 3-dimensional surfaces. The finding in this work is expected to be helpful for the study of the periodic solution in physics.

Automated summary

This study applied an ancient Chinese algorithm called Ying Bu Zu Shu to find periodic solution of the time-space fractional modified form of the complex nonlinear Fokas-Lenells equation, proving the effectiveness and reliability of the proposed method. By plotting the solutions with different fractional orders in 2-dimensional and 3-dimensional surfaces, it provides valuable insights for the study of periodic solutions in physics.