M-derivative applied to the dispersive optical solitons for the Schrödinger-Hirota equation

Abstract

Optical dispersive soliton solutions to the fractional Schrodinger-Hirota equation (SHE) in an optical fiber involving M-derivative of order $ \alpha$ are studied in this paper. The considered analytical method is based on the Jacobi elliptic function (JEF) ansatz. We found new bright, dark and singular optical soliton solutions that are relevant in optoelectronics problems in optical fibers. Some important constraints conditions were founded between the parameters of the JEF solitons solutions. The main result of the present work shows that the JEF ansatz is an important and efficient mathematical method to obtain new solutions for solving problems in optical fibers. Typical behaviour of the obtained soliton solutions is depicted in some interesting simulations.