Abundant novel solutions of the conformable Lakshmanan-Porsezian-Daniel model

Hajar Farhan Ismael; Haci Mehmet Baskonus; Hasan Bulut

doi:10.3934/dcdss.2020398

Article Contents

2021, Volume 14, Issue 7: 2311-2333. Doi: 10.3934/dcdss.2020398

This issue Previous Article New class of volterra integro-differential equations with fractal-fractional operators: Existence, uniqueness and numerical scheme Next Article Lyapunov type inequality in the frame of generalized Caputo derivatives

Abundant novel solutions of the conformable Lakshmanan-Porsezian-Daniel model

1.
Department of Mathematics, Faculty of Science, University of Zakho, Zakho, Iraq
2.
Department of Mathematics and Science Education, Harran University, Sanliurfa, Turkey
3.
Department of Mathematics, Faculty of Science, Firat University, Elazig, Turkey

^* Corresponding author: Hajar Farhan Ismael
^* Corresponding author: Hajar Farhan Ismael

Received: June 30, 2019

Revised: October 31, 2019

Early access: June 2020

Published: July 2021

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Abstract

In this paper, three images of nonlinearity to the fractional Lakshmanan Porsezian Daniel model in birefringent fibers are investigated. The new bright, periodic wave and singular optical soliton solutions are constructed via the $ \left( m+\frac{G'}{G} \right) $ expansion method, which are applicable to the dynamics within the optical fibers. All solutions are novel compared with solutions obtained via different methods. All solutions verify the conformable Lakshmanan-Porsezian-Daniel model and also, for the existence the constraint conditions are utilized. Moreover, 2D and 3D for all solutions are plotted to more understand its physical characteristics.

Keywords:

Fractional Lakshmanan-Porsezian-Daniel model,
bright,
periodic and singular solutions.

Mathematics Subject Classification: Primary: 35Q60, 35C07, 35R11; Secondary: 35C08.

Citation:

Full Text(HTML)

Figure 1. 3D graphic of Eq. (16) when $ \alpha = 0.9,{{A}_{1}} = 3,{{A}_{2}} = 2,a = 0.4,b = 0.1,\delta = 0.2,\nu = 0.2,\kappa = 0.1,\epsilon = 0.4,\beta = 0.9,\lambda = 1,m = 1,\mu = -1 $ and $ t = -2 $ for 2D

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Figure 2. 3D figure of Eq. (17), when $ \alpha = 0.8,{{A}_{1}} = 3,{{A}_{2}} = 2,a = 0.4,b = 0.1,\delta = 0.2,\nu = -0.2,\kappa = 0.1,\epsilon = 0.4,\beta = 0.8,\lambda = -1,m = 1,\mu = 1 $ and $ t = 2 $ for 2D

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Figure 3. 3D figure of Eq. (18) when $ \alpha = 0.5,{{A}_{1}} = -3,{{A}_{2}} = 0.2,a = 0.4,b = 0.1,\delta = 0.2,\nu = -0.2,\kappa = 0.5,\epsilon = 0.1,\beta = 0.5,\lambda = -2,m = 2,\mu = 1 $ and $ t = 2 $ for 2D

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Figure 4. 3D graphic of Eq. (19) when $ \alpha = 0.5,{{A}_{1}} = -3,{{A}_{2}} = 1,a = 0.3,b = -2,\delta = 0.2,\nu = 0.2,\kappa = 0.1,\epsilon = 2,\beta = 0.5,\lambda = 1,m = 1,\mu = -1 $ and $ t = -2 $ for 2D

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Figure 5. 3D figure of Eq. (20) when $ \alpha = 0.5,{{A}_{1}} = 3,{{A}_{2}} = 1,a = 0.3,b = 0.2,\delta = 0.2,\nu = -0.2,\kappa = 0.1,\epsilon = 2,\beta = 0.5,\lambda = -1,m = 1,\mu = 1 $ and $ t = 2 $ for 2D

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Figure 6. 3D figure of Eq. (21) when $ \alpha = 0.5,{{A}_{1}} = 3,{{A}_{2}} = 1,a = 0.3,b = 0.2,\delta = 0.2,\nu = -0.2,\kappa = 0.1,\epsilon = 2,\beta = 0.5,\lambda = -2,m = 2,\mu = 1 $ and $ t = 2 $ for 2D

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Figure 7. 3D figure of Eq. (26) when $ \alpha = 0.9,{{A}_{1}} = 1,{{A}_{2}} = 3,a = 0.3,b = 0.2,\delta = 0.2,\nu = 0.1,\kappa = 2,\epsilon = 0.2,{{a}_{1}} = 2,\beta = 0.9,\lambda = 1,m = 1,\mu = -1 $ and $ t = -2 $ for 2D

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Figure 8. 3D figure of Eq. (27) when $ \alpha = 0.9,{{A}_{1}} = 1,{{A}_{2}} = 3,a = 0.3,b = 0.2,\delta = 0.2,\nu = -0.1,\kappa = 2,\epsilon = 0.2,{{a}_{1}} = -2,\beta = 0.9,\lambda = -1,m = 1,\mu = 1 $ and $ t = 2 $ for 2D

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Figure 9. 3D figure of Eq. (28) when $ \alpha = 0.5,{{A}_{1}} = 3,{{A}_{2}} = 2,a = 2,b = 0.1,\delta = 0.2,\nu = 0.2,\kappa = 1,\epsilon = 0.2,{{a}_{1}} = 2,\beta = 0.5,\lambda = -2,m = 2,\mu = 1 $ and $ t = 2 $ for 2D

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Figure 10. 3D figure of Eq. (29) when $ \alpha = 0.5,{{A}_{1}} = 2,{{A}_{2}} = 3,a = 0.2,b = 0.2,\delta = 0.2,\nu = -0.2,\kappa = 1,\epsilon = 2,{{c}_{1}} = 1,\beta = 0.5,\gamma = -1,\lambda = 1,m = 1,\mu = -1 $ and $ t = 2 $ for 2D

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Figure 11. 3D figure of Eq. (30) when $ \alpha = 0.9,{{A}_{1}} = 2,{{A}_{2}} = 3,a = 3,b = -2,\delta = 0.2,\nu = 0.1,\kappa = 2,\epsilon = 0.2,{{c}_{1}} = 1,\beta = 0.9,\gamma = 1,\lambda = -1,m = 1,\mu = 1 $ and $ t = 2 $ for 2D

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Figure 12. 3D figure of Eq. (31) when $ \alpha = 0.9,{{A}_{1}} = -3,{{A}_{2}} = 2,a = 2,b = 0.1,\delta = 0.2,\nu = 0.2,\kappa = 1,\epsilon = 0.2,{{c}_{1}} = 1,\beta = 0.9,\gamma = -2,\lambda = -2,m = 2,\mu = 1 $ and $ t = 2 $ for 2D

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Figure 13. 3D figure of Eq. (36) when $ \alpha = 1/2,{{A}_{1}} = 0.2,{{A}_{2}} = 0.3,a = -0.2,b = 1,\delta = -0.2,\nu = 0.2,\kappa = 0.1,\epsilon = 0.2,{{c}_{1}} = 2,\gamma = 0.1,{{a}_{0}} = 0.1,{{c}_{3}} = 0.1,\beta = 1/2,\lambda = 1,m = 1,\mu = -1 $ and $ t = -2 $ for 2D

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Figure 14. 3D figure of Eq. (37) when $ \alpha = 0.5,{{A}_{1}} = 1,{{A}_{2}} = 3,a = -0.2,b = 2,\delta = -0.2,\nu = 0.2,\kappa = 1,\epsilon = 2,{{c}_{1}} = 1,\gamma = 1,{{a}_{0}} = 5,{{c}_{3}} = 1,\beta = 0.5,\lambda = -1,m = 1,\mu = 1 $ and $ t = -2 $ for 2D

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Figure 15. 3D figure of Eq. (38) when $ \alpha = 0.5,{{A}_{1}} = 2,{{A}_{2}} = 0.3,a = -0.2,b = 2,\delta = -0.2,\nu = 0.2,\kappa = 1,\epsilon = 2,{{c}_{1}} = 1,\gamma = 1,{{a}_{0}} = 1,{{c}_{3}} = 0.1,\beta = 0.5,\lambda = -2,m = 2,\mu = 1 $ and $ t = 2 $ for 2D

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Figure 16. 3D figure of Eq. (39) when $ \alpha = 0.5,{{A}_{1}} = 0.2,{{A}_{2}} = 0.3,b = -0.2,\delta = 0.2,\nu = 0.2,\kappa = 1,\epsilon = 2,{{c}_{1}} = 0.2,\gamma = 1,{{c}_{3}} = 1,\beta = 0.5,{{a}_{1}} = 1,\omega = 1,a = 0.2,\lambda = 1,m = 1,\mu = -1 $ and $ t = -2 $ for 2D

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Figure 17. 3D figure of Eq. (40) when $ \alpha = 0.9,{{A}_{1}} = 0.4,{{A}_{2}} = 2,b = -0.2,\delta = 0.2,\nu = 0.2,\kappa = 1,\epsilon = 2,{{c}_{1}} = 1,\gamma = 1,{{c}_{3}} = 1,\beta = 0.9,{{a}_{1}} = 0.1,\omega = 1,a = 0.2,\lambda = -1,m = 1,\mu = 1 $ and $ t = 2 $ for 2D

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Figure 18. 3D figure of Eq. (41) when $ \alpha = 0.9,{{A}_{1}} = 0.4,{{A}_{2}} = 2,b = -0.2,\delta = 0.2,\nu = 0.2,\kappa = 1,\epsilon = 2,{{c}_{1}} = 1,\gamma = 1,{{c}_{3}} = 1,\beta = 0.9,{{a}_{1}} = 0.1,\omega = 1,a = 0.2,\lambda = -2,m = 2,\mu = 1 $ and $ t = 2 $ for 2D

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