Optical solitons of conformable space-time fractional NLSE with Spatio-temporal dispersion

Abstract

In this work, the dynamics of traveling waves of an improved nonlinear space-time fractional Schrödinger's equation with spatio-temporal dispersion in addition to group-velocity dispersion are studied. This equation models the propagation of solitons through nano optical fibers. The fractional derivative form is considered in the meaning of conformable fractional derivative. The exp(−φ (ξ)) algorithm will be carried out for retrieving the optical soliton solutions containing the form of kink and multi-soliton shapes. In addition, some graphical simulations of solutions are provided for better understanding the physical phenomena.

New approximate analytical solutions for the nonlinear fractional Schrödinger equation with second‐order spatio‐temporal dispersion via double Laplace transform method

“…and Yaşar and Yaşar, 34,35 to obtain exact optical soliton solutions for modified nonlinear Schrödinger equation (MNLSE) with spatiotemporal dispersion. Finding analytical and approximate analytical solutions for the modified forms of nonlinear fractional Schrödinger equation has become a common research interest for physicists and applied mathematicians in the field of optical soliton propagation because of the applications of this equation in plasma, optics, electromagnetism, fluid dynamics, and optical communication 34,35 . The dynamics of optical soliton propagation in optical fiber can be interpreted from the MNLSE with second‐order spatiotemporal dispersion and group velocity dispersion coefficients 34 .…”

“…Various fractional formulations have been introduced in Ghanbari et al. and Yaşar and Yaşar, 34,35 to obtain exact optical soliton solutions for modified nonlinear Schrödinger equation (MNLSE) with spatiotemporal dispersion. Finding analytical and approximate analytical solutions for the modified forms of nonlinear fractional Schrödinger equation has become a common research interest for physicists and applied mathematicians in the field of optical soliton propagation because of the applications of this equation in plasma, optics, electromagnetism, fluid dynamics, and optical communication 34,35 .…”