Ismael, Hajar Farhan; Baskonus, Haci Mehmet; Bulut, Hasan Abundant novel solutions of the conformable Lakshmanan-Porsezian-Daniel model. (English) Zbl 1475.35329 Discrete Contin. Dyn. Syst., Ser. S 14, No. 7, 2311-2333 (2021). Summary: 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. Cited in 3 Documents MSC: 35Q60 PDEs in connection with optics and electromagnetic theory 35C07 Traveling wave solutions 35R11 Fractional partial differential equations 35C08 Soliton solutions Keywords:fractional Lakshmanan-Porsezian-Daniel model; bright; periodic and singular solutions PDFBibTeX XMLCite \textit{H. F. Ismael} et al., Discrete Contin. Dyn. Syst., Ser. S 14, No. 7, 2311--2333 (2021; Zbl 1475.35329) Full Text: DOI References: [1] K. K. Ali; H. F. Ismael; B. A. Mahmood; M. A. Yousif, MHD Casson fluid with heat transfer in a liquid film over unsteady stretching plate, Int. J. Adv. Appl. Sci., 4, 55-58 (2017) [2] K. K. Ali; A. Varol, Weissenberg and Williamson MHD flow over a stretching surface with thermal radiation and chemical reaction, JP J. Heat Mass Transf., 18, 57-71 (2019) [3] K. K. Ali, R. Yilmazer, A. Yokus and H. Bulut, Analytical solutions for the \((3+1)\)-dimensional nonlinear extended quantum Zakharov-Kuznetsov equation in plasma physics, Physica A: Statistical Mechanics and its Applications, 548 (2020), 124327. · Zbl 1451.35156 [4] R. T. Alqahtani; M. M. Babatin; A. Biswas, Bright optical solitons for Lakshmanan-Porsezian-Daniel model by semi-inverse variational principle, Optik, 154, 109-114 (2018) [5] A. A. AlQarni et al., Optical solitons for Lakshmanan-Porsezian-Daniel model by Riccati equation approach, Optik, 182, 922-929 (2019) [6] S. Arshed; A. Biswas; F. B. Majid; Q. Zhou; S. P. Moshokoa; M. Belic, Optical solitons in birefringent fibers for Lakshmanan-Porsezian-Daniel model using exp \(\left(-\phi(\xi) \right)\)-expansion method, Optik, 172, 651-656 (2018) [7] A. Atangana and K. M. Owolabi, New numerical approach for fractional differential equations, Math. Model. Nat. Phenom., 13 (2008), 21 pp. · Zbl 1406.65045 [8] A. Atangana and A. Kılıçman, The use of Sumudu transform for solving certain nonlinear fractional heat-like equations, Abstr. Appl. Anal., 2013 (2013), Art. ID 737481, 12 pp. · Zbl 1275.65067 [9] H. M. Baskonus; H. Bulut, On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method, Open Math., 13, 547-556 (2015) · Zbl 1350.65077 [10] H. Baskonus; T. Mekkaoui; Z. Hammouch; H. Bulut, Active control of a chaotic fractional order economic system, Entropy, 17, 5771-5783 (2015) [11] A. Biswas; M. Ekici; A. Sonmezoglu; R. T. Alqahtani, Optical solitons with differential group delay for coupled Fokas-Lenells equation by extended trial function scheme, Optik, 165, 102-110 (2018) [12] A. Biswas; M. Ekici; A. Sonmezoglu; M. M. Babatin, Optical solitons with differential group delay and dual-dispersion for Lakshmanan-Porsezian-Daniel model by extended trial function method, Optik, 170, 512-519 (2018) [13] A. Biswas et al, Optical solitons with Lakshmanan-Porsezian-Daniel model using a couple of integration schemes, Optik, 158, 705-711 (2018) [14] A. Biswas; A. H. Kara; R. T. Alqahtani; M. Z. Ullah; H. Triki; M. Belic, Conservation laws for optical solitons of Lakshmanan-Porsezian-Daniel model, Proc. Rom. Acad. Ser. A - Math. Phys. Tech. Sci. Inf. Sci., 19, 39-44 (2018) [15] A. Biswas; Y. Yldrm; E. Yaar; R. T. Alqahtani, Optical solitons for Lakshmanan-Porsezian-Daniel model with dual-dispersion by trial equation method, Optik, 168, 432-439 (2018) [16] A. Biswas; Y. Yildirim; E. Yasar; Q. Zhou; S. P. Moshokoa; M. Belic, Optical solitons for Lakshmanan-Porsezian-Daniel model by modified simple equation method, Optik, 160, 24-32 (2018) [17] C. Cattani, T. A. Sulaiman, H. M. Baskonus and H. Bulut, Solitons in an inhomogeneous Murnaghans rod, Eur. Phys. J. Plus, 133 (2018), 228. [18] H. Bulut; T. A. Sulaiman; H. M. Baskonus, Dark, bright optical and other solitons with conformable space-time fractional second-order spatiotemporal dispersion, Optik, 163, 1-7 (2018) [19] C. Cattani, T. A. Sulaiman, H. M. Baskonus and H. Bulut, On the soliton solutions to the Nizhnik-Novikov-Veselov and the Drinfeld-Sokolov systems, Opt. Quantum Electron, 50 (2018), 138. [20] L. D. Moleleki; T. Motsepa; C. M. Khalique, Solutions and conservation laws of a generalized second extended \((3+1)\)-dimensional Jimbo-Miwa equation, Appl. Math. Nonlinear Sci., 3, 459-474 (2018) · Zbl 1524.35382 [21] M. Dewasurendra; K. Vajravelu, On the method of inverse mapping for solutions of coupled systems of nonlinear differential equations arising in nanofluid flow, heat and mass transfer, Appl. Math. Nonlinear Sci., 3, 1-14 (2018) · Zbl 1524.34039 [22] M. Ekici, Optical solitons in birefringent fibers for Lakshmanan-Porsezian-Daniel model by extended Jacobis elliptic function expansion scheme, Optik, 172, 651-656 (2018) [23] M. M. A. El-Sheikh, et al., Optical solitons in birefringent fibers with Lakshmanan-Porsezian-Daniel model by modified simple equation, Optik, 192 (2019), 162899. [24] E. İ. Eskitąçıoğlu; M. B. Aktaş; H. M. Baskonus, New complex and hyperbolic forms for Ablowitz-Kaup-Newell-Segur wave equation with fourth order, Appl. Math. Nonlinear Sci., 4, 105-112 (2019) · Zbl 1524.35525 [25] E. Fan; J. Zhang, Applications of the Jacobi elliptic function method to special-type nonlinear equations, Phys. Lett. A, 305, 383-392 (2002) · Zbl 1005.35063 [26] W. Gao and H. F. Ismael, H. Bulut and H. M. Baskonus, Instability modulation for the (2+1)-dimension paraxial wave equation and its new optical soliton solutions in Kerr media, Phys. Scr., 95 (2020), 035207. [27] W. Gao, H. F. Ismael, S. A. Mohammed, H. M. Baskonus and H. Bulut, Complex and real optical soliton properties of the paraxial nonlinear Schrödinger equation in Kerr media with M-fractional, Front. Phys., 7 (2019), 197. [28] W. Gao, H. F. Ismael, A. M. Husien, H. Bulut and H. M. Baskonus, Optical soliton solutions of the Cubic-Quartic nonlinear Schrödinger and resonant nonlinear Schrödinger equation with the parabolic law, Appl. Sci., 10 (2020), 219. [29] Z. Hammouch; T. Mekkaoui, Traveling-wave solutions of the generalized Zakharov equation with time-space fractional derivatives, Journal| MESA, 5, 489-498 (2014) · Zbl 1305.35011 [30] Z. Hammouch, T. Mekkaoui and P. Agarwal, Optical solitons for the Calogero-Bogoyavlenskii-Schiff equation in (2 + 1) dimensions with time-fractional conformable derivative, Eur. Phys. J. Plus, 133 (2018), 248. [31] M. B. Hubert; et al., Optical solitons with Lakshmanan-Porsezian-Daniel model by modified extended direct algebraic method, Optik, 162, 228-236 (2018) [32] O. A. Ilhan; A. Esen; H. Bulut; H. M. Baskonus, Singular solitons in the pseudo-parabolic model arising in nonlinear surface waves, Results Phys., 12, 1712-1715 (2019) [33] H. F. Ismael, Carreau-Casson fluids flow and heat transfer over stretching plate with internal heat source/sink and radiation, Int. J. Adv. Appl. Sci., 4, 11-15 (2017) [34] H. F. Ismael; K. K. Ali, MHD casson flow over an unsteady stretching sheet, Adv. Appl. Fluid Mech., 20, 533-541 (2017) [35] H. F. Ismael; N. M. Arifin, Flow and heat transfer in a maxwell liquid sheet over a stretching surface with thermal radiation and viscous dissipation, JP J. Heat Mass Transf., 15, 847-866 (2018) [36] H. F. Ismael, H. Bulut and H. M. Baskonus, Optical soliton solutions to the Fokas-Lenells equation via sine-Gordon expansion method and \((m+ (G'/G))\)-expansion method, Pramana, 94 (2020), 35. [37] A. Javid; N. Raza, Singular and dark optical solitons to the well posed Lakshmanan-Porsezian-Daniel model, Optik, 171, 120-129 (2018) [38] A. J. M. Jawad; M. J. Abu-AlShaeer; A. Biswas; Q. Zhou; S. Moshokoa; M. Belic, Optical solitons to Lakshmanan-Porsezian-Daniel model for three nonlinear forms, Optik, 160, 197-202 (2018) [39] C. M. Khalique; I. E. Mhlanga, Travelling waves and conservation laws of a \((2+1)\)-dimensional coupling system with Korteweg-de Vries equation, Appl. Math. Nonlinear Sci., 3, 241-253 (2018) · Zbl 1524.35107 [40] C. M. Khalique and L. D. Moleleki, A \((3+ 1)\)-dimensional generalized BKP-Boussinesq equation: Lie group approach, Results Phys., 13 (2019), 102239. [41] K. Khan; M. Ali Akbar, Traveling wave solutions of the \((2 + 1)\)-dimensional Zoomeron equation and the Burgers equations via the MSE method and the Exp-function method, Ain Shams Eng. J., 5, 247-256 (2014) [42] S. Koonprasert; S. Sirisubtawee; S. Ampun, More explicit solitary solutions of the space-time fractional fifth order nonlinear Sawada-Kotera equation via the improved generalized Riccati equation mapping method, Comput. Math. with Appl., 13, 2629-2658 (2017) [43] C.-K. Kuo; B. Ghanbari, Resonant multi-soliton solutions to new \((3+1)\)-dimensional Jimbo-Miwa equations by applying the linear superposition principle, Nonlinear Dyn., 96, 459-464 (2019) · Zbl 1437.37093 [44] W. Liu; D.-Q. Qiu; Z.-W. Wu; J.-S. He, Dynamical behavior of solution in integrable nonlocal Lakshmanan - Porsezian - Daniel equation, Commun. Theor. Phys., 65, 671-676 (2016) · Zbl 1345.35104 [45] J. Manafian and M. F. Aghdaei, Abundant soliton solutions for the coupled Schrödinger-Boussinesq system via an analytical method, Eur. Phys. J. Plus, 131 (2016), 97. [46] J. Manafian, M. Foroutan and A. Guzali, Applications of the ETEM for obtaining optical soliton solutions for the Lakshmanan-Porsezian-Daniel model, Eur. Phys. J. Plus, 132 (2017), 494. [47] J. Manafian; M. Lakestani; A. Bekir, Study of the analytical treatment of the \((2+1)\)-Dimensional Zoomeron, the duffing and the SRLW equations via a new analytical approach, Int. J. Appl. Comput. Math., 2, 243-268 (2016) · Zbl 1420.35061 [48] Ö. Oruç, F. Bulut and A. Esen, Numerical solution of the KdV equation by Haar wavelet method, Pramana, 87 (2016), 94. · Zbl 1354.65194 [49] K. M. Owolabi and A. Atangana, On the formulation of Adams-Bashforth scheme with Atangana-Baleanu-Caputo fractional derivative to model chaotic problems, Chaos, 29 (2019), 023111, 12pp. · Zbl 1409.34016 [50] H. Rezazadeh; M. Mirzazadeh; S. M. Mirhosseini-Alizamini; A. Neirameh; M. Eslami; Q. Zhou, Optical solitons of Lakshmanan-Porsezian-Daniel model with a couple of nonlinearities, Optik, 164, 414-423 (2018) [51] A. R. Seadawy, D. Kumar and A. K. Chakrabarty, Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method, Eur. Phys. J. Plus, 133 (2018), 182. [52] T. A. Sulaiman; H. Bulut; A. Yokus; H. M. Baskonus, On the exact and numerical solutions to the coupled Boussinesq equation arising in ocean engineering, Indian J. Phys., 93, 647-656 (2019) [53] J. Vega-Guzman; A. Biswas; M. F. Mahmood; Q. Zhou; S. P. Moshokoa; M. Belic, Optical solitons with polarization mode dispersion for Lakshmanan-Porsezian-Daniel model by the method of undetermined coefficients, Optik, 171, 114-119 (2018) [54] J. Vega-Guzman et al., Optical solitons for Lakshmanan-Porsezian-Daniel model with spatio-temporal dispersion using the method of undetermined coefficients, Optik, 144, 115-123 (2017) [55] X.-F. Yang, Z.-C. Deng and Y. Wei, A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application, Adv. Difference Equ., 2015 (2015), 117. · Zbl 1422.35153 [56] X.-J. Yang; F. Gao; H. M. Srivastava, Exact travelling wave solutions for the local fractional two-dimensional Burgers-type equations, Comput. Math. Appl., 73, 203-210 (2017) · Zbl 1386.35460 [57] X.-J. Yang; H. M. Srivastava; C. Cattani, Local fractional homotopy perturbation method for solving fractal partial differential equations arising in mathematical physics, Rom. Reports Phys., 67, 752-761 (2015) [58] Y. Yang, Z. Yan and B. A. Malomed, Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schrödinger equation, Chaos, 25 (2015), 103112, 9pp. · Zbl 1374.35392 [59] X. Yang; Y. Yang; C. Cattani; M. Zhu, A new technique for solving the 1-D Burgers equation, Therm. Sci., 21, 129-136 (2017) [60] H. Yepez-Martínez and J. F. Gömez-Aguilar, M-derivative applied to the soliton solutions for the Lakshmanan-Porsezian-Daniel equation with dual-dispersion for optical fibers, Optical and Quantum Electronics, 51 (2019), 31. [61] A. Yokus; H. M. Baskonus; T. A. Sulaiman; H. Bulut, Numerical simulation and solutions of the two-component second order KdV evolutionarysystem, Numer. Methods Partial Differ. Equ., 34, 211-227 (2018) · Zbl 1383.65099 [62] M. A. Yousif; B. A. Mahmood; K. K. Ali; H. F. Ismael, Numerical simulation using the homotopy perturbation method for a thin liquid film over an unsteady stretching sheet, Int. J. Pure Appl. Math., 107, 289-300 (2016) [63] A. Zeeshan; H. F. Ismael; M. A. Yousif; T. Mahmood; S. U. Rahman, Simultaneous effects of slip and wall stretching/shrinking on radiative flow of magneto nanofluid through porous medium, J. Magn., 23, 491-498 (2018) [64] Z. Zheng; W. Zhao; H. Dai, A new definition of fractional derivative, Int. J. Non. Linear. Mech., 108, 1-6 (2019) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.