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Mathanaranjan, Thilagarajah. (1401). An effective technique for the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with different laws of nonlinearity. سامانه مدیریت نشریات علمی, 10(3), 701-715. doi: 10.22034/cmde.2021.46753.1964
Thilagarajah Mathanaranjan. "An effective technique for the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with different laws of nonlinearity". سامانه مدیریت نشریات علمی, 10, 3, 1401, 701-715. doi: 10.22034/cmde.2021.46753.1964
Mathanaranjan, Thilagarajah. (1401). 'An effective technique for the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with different laws of nonlinearity', سامانه مدیریت نشریات علمی, 10(3), pp. 701-715. doi: 10.22034/cmde.2021.46753.1964
Mathanaranjan, Thilagarajah. An effective technique for the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with different laws of nonlinearity. سامانه مدیریت نشریات علمی, 1401; 10(3): 701-715. doi: 10.22034/cmde.2021.46753.1964

An effective technique for the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with different laws of nonlinearity

Computational Methods for Differential Equations
مقاله 10، دوره 10، شماره 3، مهر 2022، صفحه 701-715    اصل مقاله (597.58 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.46753.1964
نویسنده
Thilagarajah Mathanaranjan*
Department of Mathematics and Statistics University of Jaffna, Sri Lanka.
چکیده
In the present study, we investigate the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with three different laws of nonlinearity namely, parabolic law, quadratic-cubic law, and weak non-local law. This model governs the propagation of solitons through nonlinear optical fibers. An effective approach namely, the exp(−Φ(ξ)) expansion method is applied to construct some new soliton solutions of the governing model. Consequently, the dark, singular, rational and periodic solitary wave solutions are successfully revealed. The comparisons with other results are also presented. In addition, the dynamical structures of obtained solutions are presented through 3D and 2D plots. 
کلیدواژه‌ها
Conformable derivative؛ Fractional cubic-quartic nonlinear Schr¨odinger equation؛ Soliton solutions؛ Exp(−Φ(ξ))-expansion method
مراجع
  • [1]         T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57-66.
  • [2]         M. A. Abdou, The extended F-expansion method and its application for a class of nonlinear evolution equations, Chaos Solitons Fractals, 31 (2007), 95-104 .
  • [3]         G. Adomian. Solving frontier problems of physics: The decomposition method. Kluwer Academic Publishers, Boston 1994.
  • [4]         H. Ahmad, M. N. Alam, and M. Omri, New computational results for a prototype of an excitable system, Results in Physics, Volume 28 2021, 104666.
  • [5]         M. N. Alam and C.Tunc, Constructions of the optical solitons and other solitons to the conformable fractional Zakharov–Kuznetsov equation with power law nonlinearity, Journal of Taibah University for Science, 14(1) (2020), 94-100.
  • [6]         M. N. Alam and X. Li, Symbolic methods to construct a cusp, breathers, kink, rogue waves and some soliton waves solutions of nonlinear partial differential equations, Computational Methods for Differential Equations, 8(3) (2020), 597-609.
  • [7]         M. N. Alam and X. Li, Exact traveling wave solutions to higher order nonlinear equations, Journal of Ocean Engineering and Science, 4(3) (2019), 276-288.
  • [8]         M. N. Alam, Exact solutions to the foam drainage equation by using the new generalized (G//G)-expansion method, Results in Physics, 5 (2015), 168-177.
  • [9]         M. N. Alam and M. Ali Akbar, The new approach of the generalized (G//G)-expansion method for nonlinear evolution equations, Ain Shams Engineering Journal, 5(2) (2014), 595-603.
  • [10]       M. N. Alam, A. Akbar, and S. T. Mohyud-Din, A novel (G//G)-expansion method and its application to the Boussinesq equation, Chinese Phys. B., 23 (2013), 020203.
  • [11]       M. N. Alam and C. Tunc, Soliton solutions to the LWME in a MEECR and DSWE of soliton and multiple soliton solutions to the longitudinal wave motion equation in a magneto-electro elastic circular rod and the Drin- feld–Sokolov–Wilson equation, Miskolc Math. Notes, 21(2) (2020), 545-561.
  • [12]       M. N. Alam and C. Tunc, New solitary wave structures to the (2 + 1)-dimensional KD and KP equations with spatio-temporal dispersion, Journal of King Saud University – Science, 32(8) (2020), 3400-3409.
  • [13]       M. N. Alam, I. Talib, O. Bazighifan, D. N. Chalishajar, and B. Almarri, An Analytical Technique Implemented in the Fractional Clannish Random Walker’s Parabolic Equation with Nonlinear Physical Phenomena, Mathematics., 9(8) (2021), 801.
  • [14]       M. N. Alam, E. Bonyah, M. F. A. Asad, M. S. Osman, and K. M. Abualnaja, Stable and functional solutions of the Klein-Fock-Gordon equation with nonlinear physical phenomena, Phys. Scr., 96 (2021), 055207.
  • [15]       A. Ali, M. A. Iqbal, Q. M. Ul-Hassan, J. Ahmad, and S. T. Mohyud-Din, An efficient technique for higher order fractional differential equation, Springer Plus, 5 (2016), 281.
  • [16]       H. Aminikhad, H. Moosaei, and M. Hajipour, Exact solutions for nonlinear partial differential equations via Exp-function method, Numer. Methods Partial Differential Equations, 26 (2009), 1427-1433.
  • [17]       A. Biswas, Y. Yildirim, E. Yasar ,Q. Zhou, S. P. Moshokoa, and M. Belic, Optical soliton perturbation with resonant nonlinear schr¨odinger’s equation having full nonlinearity by modified simple equation method, Optik, 160 (2018), 33-43.
  • [18]       A. Biswas, H. Triki, Q. Zhou, S. P. Moshokoa, M. Z. Ullah, and M. Belic, Cubic-quartic optical solitons in Kerr and power law media, Optik, 144 (2017), 357-362.
  • [19]       H. Bulut, T. A.Sulaiman, H. M. Baskonus, and T. Aktu¨rk, On the bright and singular optical solitons to the (2+ 1)-dimensional NLS and the Hirota equations, Optic Quantum Electron, 50 (2018), 134.
  • [20]       Y. Chatibi, E. H. E. Kinani, and A. Ouhadan, Lie symmetry analysis of conformable differential equations. AIMS Mathematics, 4(4) (2019), 1133-1144.
  • [21]       Y. Chatibi, E. H. E. Kinani, and A. Ouhadan, On the discrete symmetry analysis of some classical and fractional differential equations, Mathematical Methods in the Applied Sciences, (2019), 1-11.
  • [22]       Y. Chatibi, E. H. E. Kinani, and A. Ouhadan, Lie symmetry analysis and conservation laws for the time fractional Black-Scholes equation, International Journal of Geometric Methods in Modern Physics, 17(01) (2020), 2050010.
  • [23]       C. Q. Dai and J. F. Zhang, Jacobian elliptic function method for nonlinear differential difference equations, Chaos Solutions Fractals, 27 (2006), 1042-1049.
  • [24]       H. Dutta, H. Gu¨nerhan, K. K. Ali, and R. Yilmazer, Exact Soliton Solutions to the Cubic-Quartic Non-linear Schr¨odinger Equation With Conformable Derivative. Front. Phys., 8 (2020), 62.
  • [25]       E. Fan and J. Zhang, Applications of the Jacobi elliptic function method to special-type nonlinear equations, Phys. Lett. A, 305 (2002), 383-392.
  • [26]       Z. Feng, On explicit exact solutions to the compound Burgers KdV equation, Phys Lett A, 293 (2002), 57-66.
  • [27]       W. Gao, H. F. Ismael, A. M. Husien, H. Bulut, and H. M. Baskonus, Optical Soliton Solutions of the Cubic- Quartic Nonlinear Schr¨odinger and Resonant Nonlinear Schr¨odinger Equation with the Parabolic Law, Appl. Sci., 10 (2020), 219.
  • [28]       W. Gao, H. F. Ismael, A. M. Husien, H. Bulut, and H. M. Baskonus, Optical Soliton Solutions of the Cubic- Quartic Nonlinear Schr¨odinger and Resonant Nonlinear Schr¨odinger Equation with the Parabolic Law, Appl. Sci., 10 (2020), 219.
  • [29]       M. G. Hafez, Md. Nur Alam, and M. Ali Akbar, Exact traveling wave solutions to the Klein–Gordon equation using the novel (G//G)-expansion method, Results in Physics, 4 (2014), 177-184.
  • [30]       J. H. He and X. H. Wu, Exp-function method for nonlinear wave equations, Chaos Solitons Fractals, 30 (2006), 700-708.
  • [31]       K. Hosseini, F. Samadani, D. Kumar, and M. Faridi, New optical solitons of cubic-quartic nonlinear Schr¨odinger equation, Optik, 157 (2018), 1101-1105.
  • [32]       A. Irshad, N. Ahmed, U.Khan ,S. T. Mohyud-Din, I. Khan, and S. M. E. Sherif, Optical Solutions of Schr¨odinger Equation Using Extended Sinh–Gordon Equation Expansion Method, Front. Phys., 8 (2020), 73.
  • [33]       A. J. M . Jawad, M. D. Petkovic, and A. Biswas, Modified simple equation method for nonlinear evolution equations, Appl. Math. Comput., 217 (2010), 869-877.
  • [34]       R. Khalil, M. Al. Horani, A. Yousef, and M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65-70.
  • [35]       A. E. Mahmoud, E. H. M. Z. Abdelrahman, and M. M. Khater, Exact traveling wave solutions for power law and kerr law non linearity using the exp(φ( ξ)))-expansion method, Global Journal of Science Frontier Research: F Mathematics and Decision Sciences, (2014), 14.
  • [36]       T. Mathanaranjan and K. Himalini, Analytical solutions of the time-fractional non-linear Schrodinger equation with zero and non zero trapping potential through the Sumudu Decomposition method, J Sci Univ Kelaniya, 12 (2019), 21-33.
  • [37]       T. Mathanaranjan and D. Vijayakumar, Laplace Decomposition Method for Time-Fractional Fornberg-Whitham Type Equations, Journal of Applied Mathematics and Physics, 9 (2021), 260-271.
  • [38]       T. Mathanaranjan, Soliton Solutions of Deformed Nonlinear Schr¨odinger Equations Using Ansatz Method, Int. J. Appl. Comput. Math, 7 (2021), 159.
  • [39]       T. Mathanaranjan, Solitary wave solutions of the Camassa-Holm-Nonlinear Schr¨odinger Equation, Results in Physics, 19 (2020), 103549.
  • [40]       T. Mathanaranjan, Optical singular and dark solitons to the (2 + 1)-dimensional times- pace fractional nonlinear Schrdinger equation, Results in Physics, 22 (2021), 103870.
  • [41]       T. Mathanaranjan, Exact and explicit traveling wave solutions to the generalized Gardner and BBMB equations with dual high-order nonlinear terms, Partial Differential Equations in Applied Mathematics, 4 (2021), 100120.
  • [42]       M. Mirzazadeh, Soliton solutions of Davey–Stewartson equation by trial equation method and ansatz approach, Nonlinear Dyn., 82(4) (2015), 1775-1780.
  • [43]       R. Sassaman and A. Biswas, Topological and non-topological solitons of the Klein–Gordon equations in 1+ 2 dimensions, Nonlinear Dyn., 61(1–2) (2010), 23-28.
  • [44]       K. U.Tariq and A. R. Seadawy, Optical soliton solutions of higher order nonlinear Schr¨odinger equation in monomode fibers and its applications, Optik, 154 (2018), 785-98.
  • [45]       A. M.Wazwaz, A sine-cosine method for handling nonlinear wave equations, Math. Comput. Modelling, 40 (2004), 499-508.
  • [46]       A. M. Wazwaz, The tanh method for traveling wave solutions of nonlinear equations, Appl. Math. Comput., 154 (2004), 714-723.
  • [47]       A. M. Wazwaz, Exact solutions to the double sinh-Gordon equation by the tanh method and a variable separated ODE. method, Comput. Math. Appl., 50 (2005), 1685-1696.
  • [48]       E. H. M. Zahran, Exact traveling wave solution for nonlinear fractional partial differential equation arising in soliton using the exp(φ( ξ)))-expansion method, Int. J. Comput. Appl., 109(13) (2015), 12-17.
  • [49]       E. M. E. Zayed Alzahrani and M. R. Belic, Cubic-quartic optical solitons and conservation laws with kudryashovs sextic power-law of refractive index, Optik, 227 (2021), 166059.
  • [50]       E. M. E. Zayed, M. E. M. Alngar, A. Biswas, Y. Yıldırım, P. Guggilla, S. Khan, A. K. Alzahrani, and M. R. Belic, Cubic–quartic optical soliton perturbation with lakshmanan–porsezian– daniel model, Optik, 233 (2021), 166385.
  • [51]       E. M. E. Zayed, M. E. M. Alngar, A. Biswas, Y. Yıldırım, S. Khan, A. K. Alzahrani, and M. R. Belic, Cubic–quartic optical soliton perturbation in polarization-preserving fibers with fokas–lenells equation, Optik, 234 (2021), 166543.
  • [52]       E. M. E. Zayed, R. M. A. Shohib, K. A. Gepreel, M. M. El-Horbaty, and M. E. M. Alngar, Cubic-quartic optical soliton perturbation biswas-milovic equation with kudryashovs law of refractive index using two integration methods, Optik, 239 (2021), 166871.
  • [53]       E. M. E. Zayed, R. M. A. Shohib, and M. E. M. Alngar, Cubic–quartic nonlinear Schr¨odinger equation in birefringent fibers with the presence of perturbation terms, Waves in Random and Complex Media, (2020).
  • [54]       E. M. E. Zayed, M.El-Horbaty, and M. E. M. Alngar, Cubic-quartic optical soliton perturbation having four laws non-linearity with a prolific integration algorithm, Optik, 220 (2020), 165121.
  • [55]       E. M. E. Zayed and A. G. Al-Nowehy, Solitons and other exact solutions for a class of nonlinear Schr¨odinger-type equations, Optik, 130 (2017), 1295-1311.
  • [56]       E. M. E. Zayed and S. A. Hoda Ibrahim, Exact solutions of nonlinear evolution equation in mathematical physics using the modified simple equation method, Chin. Phys. Lett., 29 (2012), 060201-4.
  • [57]       X. Zeng and X. Yong, A new mapping method and its applications to nonlinear partial differential equations, Phys. Lett. A, 372 (2008), 6602-6607.
  • [58]       J. L. Zhang, M. L. Wang, Y. M. Wang, and Z. D. Fang, The improved F-expansion method and its applications, Phys.Lett.A, 350 (2006), 103-109.
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