The complex hyperbolic Schrodinger dynamical equation with a truncated M-fractional by using simplest equation method

Document Type : Research Paper

Authors

1 Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Pakistan.

2 Math Center, House no 87 Rahmanyia colony, Vehari, Pakistan.

3 Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran.

4 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.

Abstract

This article studies a complex hyperbolic Schrodinger dynamical equation that is associated with nonlinear media via ultra short pulse propagation. The modified simplest equation method is executed to construct complex solitary wave and other solutions of the aforesaid equation by considering it in conformable M-fractional derivative sense. The acquired solutions are in the form of solitary and periodic waves and rational functions. These solutions are also described with their graphical representations by assuming appropriate values of required parameters. Moreover, the results show that the aforesaid approach can be effective for solving such nonlinear Schrodinger equations arising in nonlinear optics and physical sciences.

Keywords

References

  • [1] S. Abbagari, A. Houwe, L. Akinyemi, Y. Saliou, and T. B. Bouetou, Modulation instability gain and discrete soliton interaction in gyrotropic molecular chain, Chaos Solit. Fractals., 160 (2022), 112255.
  • [2] H. Ahmad, T. A. Khan, P. S. Stanimirovic, W. Shatanawi, and T. Botmart, New approach on conventional solutions to nonlinear partial differential equations describing physical phenomena, Results Phys., 41 (2022), 105936.
  • [3] H. Ahmad, N. Alam, and M. Omri, New computational results for a prototype of an excitable system, Results Phys., 28 (2021), 104666.
  • [4] G. Ai-Lin and L. Ji, Exact solutions of (2+ 1)-dimensional hnls equation, Commun Theor Phys., 54(3) (2010), 401.
  • [5] L. Akinyemi, M. Mirzazadeh, and K. Hosseini, Solitons and other solutions of perturbed nonlinear Biswas-Milovic equation with Kudryashov’s law of refractive index, Nonlinear Analysis-Model., 27 (2022), 1-17.
  • [6] G. Akram, M. Sadaf, and I. Zainab, Observations of fractional effects of φ-derivative and M-truncated derivative for space time fractional Phi-4 equation via two analytical techniques, Chaos Solit. Fractals., 154 (2022), 111645.
  • [7] G. Akram, M. Sadaf, and M. A. U. Khan, Soliton solutions of the resonant nonlinear Schrödinger equation using modified auxiliary equation method with three different nonlinearities, Math. Comput. Simul., 206 (2023), 1-20.
  • [8] A. I. Aliyu, M. Inc, A. Yusuf, and D. Baleanu, Optical solitary waves and conservation laws to the (2+ 1)- dimensional hyperbolic nonlinear schrodinger equation, Mod Phys Lett B., 32(30) (2018, 1850373.
  • [9] W. O. Apeanti, A. R Seadawy, and D. Lu, Complex optical solutions and modulation instability of hyperbolic schrödinger dynamical equation, Results Phys., 12 (2019, 2091-2097.
  • [10] M. Arshad, Aly R Seadawy, and D. Lu, Elliptic function and solitary wave solutions of the higher-order nonlinear schrodinger dynamical equation with fourth-order dispersion and cubic-quintic nonlinearity and its stability, EPJ Plus, 132(8) (2017), 1-11.
  • [11] M. Arshad, A. R Seadawy, and D. Lu, Modulation stability and optical soliton solutions of nonlinear schrodinger equation with higher order dispersion and nonlinear terms and its applications, Superlattices Microstruct., 112 (2017), 422-434.
  • [12] S. Arshed, N. Raza, and M. Alansari, Soliton solutions of the generalized Davey-Stewartson equation with full nonlinearities via three integrating schemes,Ain Shams Eng. J., 12(3) (2021), 3091-3098.
  • [13] M. I. Asjad, W. A. Faridi, S. E. Alhazmi, and A. Hussanan, The modulation instability analysis and generalized fractional propagating patterns of the Peyrard-Bishop DNA dynamical equation, Opt Quantum Electron., 55(3) (2023), 1-34.
  • [14] B. Ayhan and A. Bekir, The ( Gt )-expansion method for the nonlinear lattice equations, Commun. Nonlinear Sci. Numer. Simul., 17(9) (2012), 3490-3498.
  • [15] A. Bekir and O. Guner, Exact solutions of distinct physical structures to the fractional potential kadomtsev- petviashvili equation, Comput. Methods Differ. Equ., 2(1) (2014), 26-36.
  • [16] A. Bekir and A. El Achab, Exact solutions of the 2d ginzburg-landau equation by the first integral method, Comput. Methods Differ. Equ., 2(2) (2014), 69-76.
  • [17] A. Bekir, E. Aksoy, and A. C Cevikel, Exact solutions of nonlinear time fractional partial differential equations by sub-equation method, Math. Methods Appl. Sci., 38(13) (2015), 2779-2784.
  • [18] N. Cheemaa, S. Chen, and A. R Seadawy, Propagation of isolated waves of coupled nonlinear (2+ 1)-dimensional maccari system in plasma physics, Results Phys., 17 (2020), 102987.
  • [19] C. Chen and Y. L. Jiang, Simplest equation method for some time-fractional partial differential equations with conformable derivative, Comput. Math. with Appl., 75(8) (2018), 2978-2988.
  • [20] A. C Cevikel, A. Bekir, S. San, and M. B Gucen, Construction of periodic and solitary wave solutions for the complex nonlinear evolution equations, J. Frankl. Inst., 351(2) (2014), 694-700.
  • [21] MA Helal, Aly R Seadawy, and MH Zekry, Stability analysis of solitary wave solutions for the fourthorder nonlinear boussinesq water wave equation, Appl. Math. Comput., 232 (2014), 1094-1103.
  • [22] K. Hosseini, A. Bekir, and M. Kaplan, New exact traveling wave solutions of the tzitzeicatype evolution equations arising in non-linear optics, J. Mod. Opt., 64(16) (2017), 1688-1692.
  • [23] M. Iqbal, A. R Seadawy, O. H Khalil, and D. Lu, Propagation of long internal waves in density stratified ocean for the (2+ 1)-dimensional nonlinear nizhnik-novikov-vesselov dynamical equation, Results Phys., 16 (2020), 102838.
  • [24] A. Jabbari, H. Kheiri, and A. Bekir.Exact solutions of the coupled higgs equation and the maccari system using he’s semi-inverse method and ( Gt )-expansion method, Comput. Math. with Appl., 62(5) (2011), 2177-2186.
  • [25] D. Lu, A. R. Seadawy, and A. Ali, Dispersive traveling wave solutions of the equal-width and modified equal-width equations via mathematical methods and its applications, Results Phys., 9 (2018), 313-320.
  • [26] D. Lu, A. R Seadawy, and A. Ali, Applications of exact traveling wave solutions of modified liouville and the symmetric regularized long wave equations via two new techniques, Results Phys., 9 (2018), 1403-1410.
  • [27] F. Mainardi and R. Gorenflo, On mittag-lffler-type functions in fractional evolution processes, J. Comput. Appl. Math., 118 (1-2) (2000), 283-299.
  • [28] S. Z. Majid, W. A. Faridi, M. I. Asjad, A. El-Rahman, and S. M. Eldin, Explicit Soliton Structure Formation for the Riemann Wave Equation and a Sensitive Demonstration, Fractal fract. 7(2) (2023), 102.
  • [29] MS Osman, A. Zafar, K. K Ali, and W. Razzaq, Novel optical solitons to the perturbed gerdjikov-ivanov equation with truncated m-fractional conformable derivative, Optik, 222 (2020), 165418.
  • [30] Y. S. Ozkan, E. Yasar, and A. R Seadawy, A third-order nonlinear schrodinger equation: the exact solutions, group-invariant solutions and conservation laws, J. Taibah Univ. Sci., 14(1) (2020), 585-97.
  • [31] N. Raza, Z. Hassan, and J. F. Gomez-Aguilar, Extraction of new super-Gaussian solitons via collective variables, Opt Quantum Electron., 53(8) (2021), 1-15.
  • [32] H. Rezazadeh, D. Kumar, T. A. Sulaiman, and H. Bulut, New complex hyperbolic and trigonometric solutions for the generalized conformable fractional Gardner equation, Mod Phys Lett B., 33(17) (2019), 1950196.
  • [33] S. T. Rizvi, A. R. Seadawy, S. Ahmed, and K. Ali, Einstein’s vacuum field equation: lumps, manifold periodic, generalized breathers, interactions and rogue wave solutions, Opt Quantum Electron., 55(2) (2023), 1-25.
  • [34] S. T. Rizvi, A. R. Seadawy, S. K. Naqvi, and S. O. Abbas, Study of mixed derivative nonlinear Schrödinger equation for rogue and lump waves, breathers and their interaction solutions with Kerr law, Opt Quantum Electron., 55 (2) (2023), 177 .
  • [35] A. R Seadawy, Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary- wave solutions via mathematical methods, EPJ Plus, 132(12) (2017), 1-11.
  • [36] A. R Seadawy, M. Iqbal, and D. Lu, Nonlinear wave solutions of the kudryashov-sinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity, J. Taibah Univ. Sci., 13(1) (2019), 1060-1072.
  • [37] A. R Seadawy, D. Kumar, and A. K. Chakrabarty, Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear schrodinger equations via the extended sinh-gordon equation expansion method, EPJ Plus, 133(5) (2018), 182.
  • [38] A. R Seadawy and N. Cheemaa, Propagation of nonlinear complex waves for the coupled nonlinear schrodinger equations in two core optical fibers, Physica A., 529 (2019), 121330.
  • [39] M. S. Shehata, H. Rezazadeh, E. H. Zahran, E. Tala-Tebue, and A. Bekir, New optical soliton solutions of the perturbed Fokas-Lenells equation, Commun Theor Phys., 71(11) (2019), 1275.
  • [40] F. Tascan and A. Bekir, Periodic and solitary wave solutions of complex nonlinear evolution equations by using first integral method, Int. J. Nonlinear Sci. Numer. Simul., 14(5) (2013), 255-260.
  • [41] X. Yuan-Fen, Bifurcations of exact traveling wave solutions for (2+ 1)-dimensional hnls equation, Commun Theor Phys., 57 (2012).
  • [42] A. Zafar, M Raheel, K. K Ali, and W. Razzaq, On optical soliton solutions of new hamiltonian amplitude equation via jacobi elliptic functions, EPJ Plus, 135(8) (2020), 1-17.
  • [43] A. Zafar and A. R Seadawy, The conformable space-time fractional mkdv equations and their exact solutions, J King Saud Univ Sci., 31(4) (2019), 1478-1484.
  • [44] A. Zafar, M. Raheel, A. Bekir, and W. Razzaq,The conformable space-time fractional fokas-lenells equation and its optical soliton solutions based on three analytical schemes, Int. J. Mod. Phys. B., 35(1) (2020), 2150004.
  • [45] EME. Zayed, and A.G. Al-Nowehy,Exact solutions and optical soliton solutions for the (2+ 1)-dimensional hy- perbolic nonlinear schrodinger equation, Optik, 127(12) (2016), 4970-4983.
Computational Methods for Differential Equations
Volume 12, Issue 1
January 2024
Pages 44-55

Files

History

  • Receive Date: 30 May 2020
  • Revise Date: 30 March 2023
  • Accept Date: 24 April 2023

Share

How to cite

Statistics