Abstract
This study, using the extended simplest method of equation, examines the explicit movement solutions of both the Schwarzian Korteweg-de Vries (SKdV) and (2 + 1)-Ablowitz-Kaup-Newell-Segur (AKNS.) equation. These models show the movement of the waves in optical fiber mathematically. The SKdV equation explains the movement of the isolated waves in diverse fields and on the site in a small space microsection. Some solutions obtained have been developed to show the physical and dynamic behaviors of these solutions in the obtained wave.
Highlights
Partial differential equations (PDEs) have been playing an essential role in describing and studying some complex phenomena in distinct branches of science [1,2,3,4,5]. ese phenomena have been formulated in nonlinear PDEs with an integer order or fractional order [6,7,8]
We investigate two primary mathematical models in the optical fiber via the extended simplest equation method. e first model is Atangana conformable fractional Schwarzian Korteweg-de Vries (SKdV) equation that was derived by Krichever and Novikov in the following form [25]: Dqt U +Uxx −
We study a new form of equation (2) that is given in the following system [27]: Journal of Mathematics
Summary
Partial differential equations (PDEs) have been playing an essential role in describing and studying some complex phenomena in distinct branches of science [1,2,3,4,5]. ese phenomena have been formulated in nonlinear PDEs with an integer order or fractional order [6,7,8]. We investigate two primary mathematical models in the optical fiber via the extended simplest equation method. E first model is Atangana conformable fractional SKdV equation that was derived by Krichever and Novikov in the following form [25]: Dqt U +Uxx − Equation (1) is given by [26]
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