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

  • * Corresponding author: Hajar Farhan Ismael

    * Corresponding author: Hajar Farhan Ismael 
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  • 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.

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

    Citation:

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  • 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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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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