Journal of Applied Science and Engineering

Published by Tamkang University Press

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Shengguang PengThis email address is being protected from spambots. You need JavaScript enabled to view it.

School of Engineering and Management, Pingxiang University,Pingxiang337055, Jiangxi, China


 

Received: January 3, 2023
Accepted: April 6, 2023
Publication Date: June 13, 2023

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.


Download Citation: ||https://doi.org/10.6180/jase.202401_27(1).0009  


Over the last few years, differential equations with partial derivatives have become more popular using various analytical techniques. There will be a simple method called the generalized exponential rational function method incorporated in this paper that is intended to help find subfamilies of analytical solutions to the modified (2+1)-dimensional Schrödinger equation in plasma physics. We plot several 3D figures to explain the behaviors of the results. It is shown that the methods we used in this paper can be assumed to be an efficient methodologies for solving the model. In comparison to the papers that considered our equation, our results are different achievements for the calculated equation that have not been introduced before. Moreover, it should be noted that the implemented method enables us to solve different forms of nonlinear problems.


Keywords: nonlinear equations; formal structures; closed-form, plasma, nonlinear waves


  1. [1] H. Rezazadeh, M. Odabasi, K. Tariq, R. Abazari, and H. Baskonus, (2021) “On the conformable nonlinear Schrödinger equation with second order spatiotemporal and group velocity dispersion coefficients" Chinese Journal of Physics 72: 403–414.
  2. [2] S. Rezaei, S. Rezapour, J. Alzabut, R. de Sousa, B. Alotaibi, and S. El-Tantawy, (2022) “Some novel approaches to analyze a nonlinear Schrödinger’s equation with group velocity dispersion: Plasma bright solitons" Results in Physics 105316:
  3. [3] M. Eslami, (2016) “Exact traveling wave solutions to the fractional coupled nonlinear Schrödinger equations" Applied Mathematics and Computation 285: 141–148.
  4. [4] T. Sulaiman, (2020) “Three-component coupled nonlinear Schrödinger equation: optical soliton and modulation instability analysis" Physica Scripta 95(6): 065201.
  5. [5] M. Ilie, J. Biazar, and Z. Ayati, (2018) “Resonant solitons to the nonlinear Schrödinger equation with different forms of nonlinearities" Optik 164: 201–209.
  6. [6] M. Mirzazadeh, M. Eslami, B. Vajargah, and A. Biswas, (2014) “Optical solitons and optical rogons of generalized resonant dispersive nonlinear Schrödinger’s equation with power law nonlinearity" Optik 125(16): 4246–4256.
  7. [7] K.Wang and G.Wang, (2021) “Variational theory and new abundant solutions to the (1+2)-dimensional chiral nonlinear Schrödinger equation in optics" Physics Letters A 412: 127588.
  8. [8] M. Eslami and H. Rezazadeh, (2016) “The first integral method for Wu-Zhang system with conformable time-fractional derivative" Calcolo 53(3): 475–485.
  9. [9] A. R. Seadawy and N. Cheemaa, (2020) “Some new families of spiky solitary waves of one-dimensional higherorder K − dV equation with power law nonlinearity in plasma physics" Indian Journal of Physics 94(1): 117–126.
  10. [10] A. R. Seadawy, (2014) “Stability analysis for Zakharov-Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma" Computers & Mathematics with Applications 67(1): 172˘180.
  11. [11] S. T. R. Rizvi, A. R. Seadawy, F. Ashraf, M. Younis, H. Iqbal, and D. Baleanu, (2020) “Lump and interaction solutions of a geophysical Korteweg-de Vries equation" Results in Physics 19: 103661.
  12. [12] M. Marin, A. Seadawy, S. Vlase, and A. Chirila, (2022) “On mixed problem in thermoelasticity of type III for Cosserat media" Journal of Taibah University for Science 16(1): 1264–1274.
  13. [13] M. Eslami and H. Rezazadeh, (2016) “The first integral method for Wu-Zhang system with conformable time-fractional derivative" Calcolo 53(3): 475–485.
  14. [14] Y. Asghari, M. Eslami, and H. Rezazadeh, (2023) “Soliton solutions for the time-fractional nonlinear differential difference equation with conformable derivatives in the ferroelectric materials" Optical and Quantum Electronics 55(4): 289.
  15. [15] Y. Asghari, M. Eslami, and H. Rezazadeh, (2023) “Exact solutions to the conformable timefractional discretized mKdv lattice system using the fractional transformation method" Optical and Quantum Electronics 55(4): 318.
  16. [16] M. Bilal and J. Ahmad, (2022) “A variety of exact optical soliton solutions to the generalized (2+1)-dimensional dynamical conformable fractional Schrödinger model" Results in Physics: 105198.
  17. [17] H. Rezazadeh, (2018) “New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity" Optik 167: 218–227.
  18. [18] H. Aminikhah, A. R. Sheikhani, and H. Rezazadeh, (2015) “Exact solutions for the fractional differential equations by using the first integral method" Nonlinear engineering 4(1): 15–22.
  19. [19] H. Rezazadeh, D. Kumar, T. A. Sulaiman, and H. Bulut, (2019) “New complex hyperbolic and trigonometric solutions for the generalized conformable fractional Gardner equation" Modern Physics Letters B 33(17): 1950196.
  20. [20] B. Xu and S. Zhang, (2021) “Riemann-Hilbert Approach for Constructing Analytical Solutions and Conservation Laws of a Local Time-Fractional Nonlinear Schrödinger Type Equation" Symmetry 13(9): 1593.
  21. [21] B. Xu and S. Zhang, (2022) “Analytical Method for Generalized Nonlinear Schrödinger Equation with Time-Varying Coefficients: Lax Representation, Riemann-Hilbert Problem Solutions" Mathematics 10(7): 1043.
  22. [22] S. Zhang, Y. Li, and B. Xu, (2023) “Solitons, rogon solitons and their propagations and reflections in three-component coupled nonlinear Schrödinger equation" Optik 272: 170338.
  23. [23] M. Marin, A. Seadawy, S. Vlase, and A. Chirila, (2022) “On mixed problem in thermoelasticity of type III for Cosserat media" Journal of Taibah University for Science 16(1): 1264–1274.
  24. [24] I. Ahmed, A. Seadawy, and D. Lu, (2019) “Kinky breathers, W-shaped and multi-peak solitons interaction in (2+ 1)-dimensional nonlinear Schrödinger equation with Kerr law of nonlinearity" The European Physical Journal Plus 134: 1–10.
  25. [25] B. Ghanbari and M. Inc, (2018) “A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation" The European Physical Journal Plus 133(4): 1–18.
  26. [26] M. Osman and B. Ghanbari, (2018) “New optical solitary wave solutions of FokasLenells equation in presence of perturbation terms by a novel approach" Optik 175: 328˘333.
  27. [27] B. Ghanbari, D. Baleanu, and M. Al Qurashi, (2019) “New exact solutions of the generalized Benjamin-Bona-Mahony equation" Symmetry 11(1): 20.
  28. [28] B. Ghanbari and J. Gomez-Aguilar, (2019) “Optical soliton solutions for the nonlinear Radhakrishnan-Kundu-Lakshmanan equation" Modern Physics Letters B 33(32): 1950402.
  29. [29] B. Ghanbari, (2021) “On novel nondifferentiable exact solutions to local fractional Gardner’s equation using an effective technique" Mathematical Methods in the Applied Sciences 44(6): 4673–4685.
  30. [30] H. F. Ismael, H. Bulut, and H. M. Baskonus, (2021) “W-shaped surfaces to the nematic liquid crystals with three nonlinearity laws" Soft Computing 25(6): 4513–4524.
  31. [31] B. Ghanbari, A. Yusuf, and D. Baleanu, (2019) “The new exact solitary wave solutions and stability analysis for the (2+1)-dimensional Zakharov-Kuznetsov equation" Advances in difference equations 2019(1): 1–15.
  32. [32] B. Ghanbari and C. Kuo, (2021) “Abundant wave solutions to two novel KP-like equations using an effective integration method" Physica Scripta 96(4): 045203.
  33. [33] S. Kumar, M. Niwas, and I. Hamid, (2021) “Lie symmetry analysis for obtaining exact soliton solutions of generalized Camassa-Holm-Kadomtsev-Petviashvili equation" International Journal of Modern Physics B 35(02): 2150028.
  34. [34] B. Ghanbari and A. Akgül, (2020) “Abundant new analytical and approximate solutions to the generalized Schamel equation" Physica Scripta 95(7): 075201.
  35. [35] B. Ghanbari, (2022) “On the nondifferentiable exact solutions to Schamel’s equation with local fractional derivative on Cantor sets" Numerical Methods for Partial Differential Equations 38(5): 1255–1270.
  36. [36] B. Ghanbari, (2021) “Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative" Mathematical Methods in the Applied Sciences 44(11): 8759–8774.
  37. [37] B. Ghanbari and D. Baleanu, (2023) “Applications of two novel techniques in finding optical soliton solutions of modified nonlinear Schrödinger equations" Results in Physics 44: 106171.
  38. [38] B. Ghanbari and L. Rada, (2019) “Solitary wave solutions to the Tzitzeica type equations obtained by a new efficient approach" Journal of Applied Analysis & Computation 9(2): 568–589.
  39. [39] B. Ghanbari and J. Gomez-Aguilar, (2019) “New exact optical soliton solutions for nonlinear Schrödinger equation with second-order spatio-temporal dispersion involving M-derivative" Modern Physics Letters B 33(20): 1950235.
  40. [40] J.-H. He and X.-H. Wu, (2006) “Construction of solitary solution and compacton-like solution by variational iteration method" Chaos, Solitons & Fractals 29(1): 108–113.
  41. [41] S. Zhang, (2007) “Exp-function method for solving Maccari’s system" Physics Letters A 371(1-2):65–71.