Journal of Applied Science and Engineering

Published by Tamkang University Press

1.30

Impact Factor

2.10

CiteScore

Jun Ma

Jilin Institute of Chemical Technology


 

Received: July 14, 2022
Accepted: October 26, 2022
Publication Date: December 14, 2022

 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.202309_26(9).0012  


In this work, we propose the technique of a new Kudryashov for finding new traveling wave (TW) of three practical problems arising in cold plasma, namely, the modified Benjamin–Bona–Mahony (BBM) equation, the Zakharov -Kuznetsov-Modified Equal-Width (ZK-MEW) equation, and the modified Korteweg–De VriesKadomtsev-Petviashvili (KdV–KP) equation. Graphical representation for the acquired solution is presented through 3-D plots which variable parameters to show the efficiency and simplicity of the technique used. From these plots, the techniques prove to be a reliable and effective approach for solving nonlinear similar problems and can be accounted for in the near future for possible application to similar models.


Keywords: New Kudryashov Technique; Modified BBM equation; ZK-MEW equation; Modified KdV–KP equation


  1. [1] H. Qin, M. Khater, and R. A. Attia, (2020) “Inelastic interaction and blowup new solutions of nonlinear and dispersive long gravity waves" Journal of Function Spaces 2020: DOI: 10.1155/2020/5362989.
  2. [2] D. Kumar and M. Kaplan, (2018) “New analytical solutions of (2+ 1)-dimensional conformable time fractional Zoomeron equation via two distinct techniques" Chinese journal of physics 56(5): 2173–2185. DOI: 10.1016/j.cjph.2018.09.013.
  3. [3] K. Hosseini, A. Korkmaz, A. Bekir, F. Samadani, A. Zabihi, and M. Topsakal, (2021) “New wave form solutions of nonlinear conformable time-fractional Zoomeron equation in (2+ 1)-dimensions" Waves in Random and Complex Media 31(2): 228–238. DOI: 10.1080/17455030.2019.1579393.
  4. [4] H. Rezazadeh, (2018) “New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity" Optik 167: 218–227. DOI: 10.1016/j.ijleo.2018.04.026.
  5. [5] H. Ahmad, M. N. Alam, and M. Omri, (2021) “New computational results for a prototype of an excitable system" Results in Physics 28: 104666. DOI: 10.1016/j.rinp.2021.104666.
  6. [6] S.-W. Yao, L. Akinyemi, M. Mirzazadeh, M. Inc, K. Hosseini, and M. ¸Senol, (2021) “Dynamics of optical solitons in higher-order Sasa–Satsuma equation" Results in Physics 30: 104825. DOI: 10.1016/j.rinp.2021.104825.
  7. [7] M. Hashemi, (2021) “A novel approach to find exact solutions of fractional evolution equations with non-singular kernel derivative" Chaos, Solitons & Fractals 152:111367. DOI: 10.1016/j.chaos.2021.111367.
  8. [8] A. Yusuf, T. A. Sulaiman, M. Inc, S. Abdel-Khalek, and K. Mahmoud, (2021) “M- truncated optical soliton and their characteristics to a nonlinear equation governing the certain instabilities of modulated wave trains":
  9. [9] H. U. Rehman, N. Ullah, and M. Imran, (2021) “Exact solutions of Kudryashov–Sinelshchikov equation using two analytical techniques" The European Physical Journal Plus 136(6): 1–13.
  10. [10] M. Nuruzzaman, D. Kumar, and G. C. Paul, (2021) “Fractional low-pass electrical transmission line model: Dynamic behaviors of exact solutions with the impact of fractionality and free parameters" Results in Physics 27: 104457.
  11. [11] A. Yoku¸s, H. Durur, T. A. Nofal, H. Abu-Zinadah, M. Tuz, and H. Ahmad, (2020) “Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation" Open Physics 18(1): 1003–1010.
  12. [12] R. Cimpoiasu, (2020) “Multiple invariant solutions of the 3 D potential Yu–Toda–Sasa–Fukuyama equation via symmetry technique" International Journal of Modern Physics B 34(20): 2050188.
  13. [13] N. A. Kudryashov, (2012) “One method for finding exact solutions of nonlinear differential equations" Communications in Nonlinear Science and Numerical Simulation 17(6): 2248–2253.
  14. [14] N. A. Kudryashov, (2020) “Method for finding highly dispersive optical solitons of nonlinear differential equations" Optik 206: 163550.
  15. [15] N. A. Kudryashov, (2020) “Solitary wave solutions of hierarchy with non-local nonlinearity" Applied Mathematics Letters 103: 106155.
  16. [16] N. A. Kudryashov and E. V. Antonova, (2020) “Solitary waves of equation for propagation pulse with power nonlinearities" Optik 217: 164881.
  17. [17] N. A. Kudryashov, D. V. Safonova, and A. Biswas, (2019) “Painlevé Analysis and a Solution to the Traveling Wave Reduction of the Radhakrishnan—Kundu—Lakshmanan Equation" Regular and Chaotic Dynamics 24(6): 607–614.
  18. [18] N. A. Kudryashov, (2022) “Exact solutions of the complex Ginzburg–Landau equation with law of four powers of nonlinearity" Optik 265: 169548.
  19. [19] 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.
  20. [20] 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.
  21. [21] M. S. Shehata, H. Rezazadeh, E. H. Zahran, E. Tala-Tebue, and A. Bekir, (2019) “New optical soliton solutions of the perturbed Fokas-Lenells equation" Communications in Theoretical Physics 71(11): 1275.
  22. [22] H. Aminikhah, A. H. R. Sheikhani, and H. Rezazadeh, (2016) “Travelling wave solutions of nonlinear systems of PDEs by using the functional variable method" Boletim da sociedade paranaense de matemática 34(2): 213–229.
  23. [23] M. Eslami and H. Rezazadeh, (2016) “The first integral method for Wu–Zhang system with conformable timefractional derivative" Calcolo 53(3): 475–485.
  24. [24] G.Wang, K. Yang, H. Gu, F. Guan, and A. Kara, (2020) “A (2+ 1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions" Nuclear Physics B 953: 114956.
  25. [25] G.Wang, (2021) “A new (3+ 1)-dimensional Schrödinger equation: derivation, soliton solutions and conservation laws" Nonlinear Dynamics 104(2): 1595–1602.
  26. [26] G. Wang, (2021) “A novel (3+ 1)-dimensional sine-Gorden and a sinh-Gorden equation: derivation, symmetries and conservation laws" Applied Mathematics Letters 113: 106768.
  27. [27] G. Wang, (2021) “Symmetry analysis, analytical solutions and conservation laws of a generalized KdV–Burgers–Kuramoto equation and its fractional version"Fractals 29(04): 2150101.
  28. [28] G. Wang and A.-M. Wazwaz, (2022) “On the modified Gardner type equation and its time fractional form" Chaos, Solitons & Fractals 155: 111694.
  29. [29] N. A. Kudryashov, (2022) “Exact solutions of equation for description of embedded solitons" Optik 268: 169801.
  30. [30] G. Wang, A.-M. Wazwaz, et al., (2022) “A new (3+ 1)- dimensional KdV equation and mKdV equation with their corresponding fractional forms" FRACTALS (fractals) 30(04): 1–8.
  31. [31] N. A. Kudryashov, (2022) “Stationary solitons of the generalized nonlinear Schrödinger equation with nonlinear dispersion and arbitrary refractive index" Applied Mathematics Letters 128: 107888.
  32. [32] Y. Fang, G.-Z. Wu, N. A. Kudryashov, Y.-Y. Wang, and C.-Q. Dai, (2022) “Data-driven soliton solutions and model parameters of nonlinear wave models via the conservation-law constrained neural network method" Chaos, Solitons & Fractals 158: 112118.
  33. [33] N. A. Kudryashov, (2022) “Bright and dark solitons in a nonlinear saturable medium" Physics Letters A 427: 127913.
  34. [34] W. B. Rabie and H. M. Ahmed, (2022) “Optical solitons for multiple-core couplers with polynomial law of nonlinearity using the modified extended direct algebraic method" Optik 258: 168848.
  35. [35] A. Houwe, M. Inc, S. Doka, B. Acay, and L. Hoan, (2020) “The discrete tanh method for solving the nonlinear differential-difference equations" International Journal of Modern Physics B 34(19): 2050177.
  36. [36] T. B. Benjamin, J. L. Bona, and J. J. Mahony, (1972) “Model equations for long waves in nonlinear dispersive systems" Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 272(1220): 47–78.
  37. [37] M. Osman, B. Ghanbari, and J. Machado, (2019) “New complex waves in nonlinear optics based on the complex Ginzburg-Landau equation with Kerr law nonlinearity" The European Physical Journal Plus 134(1): 1–10.
  38. [38] T. B. Benjamin, J. L. Bona, and J. J. Mahony, (1972) “Model equations for long waves in nonlinear dispersive systems" Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 272(1220): 47–78.
  39. [39] C. M. Khalique and K. R. Adem, (2011) “Exact solutions of the (2+ 1)-dimensional Zakharov–Kuznetsov modified equal width equation using Lie group analysis" Mathematical and Computer Modelling 54(1-2):184–189.
  40. [40] A.-M.Wazwaz, (2008) “Solitons and singular solitons for the Gardner–KP equation" Applied Mathematics and Computation 204(1): 162–169.
  41. [41] S. M. Mirhosseini-Alizamini, N. Ullah, J. Sabi’u, H. Rezazadeh, and M. Inc, (2021) “New exact solutions for nonlinear Atangana conformable Boussinesq-like equations by new Kudryashov method" International Journal of Modern Physics B 35(12): 2150163.


    



 

2.1
2023CiteScore
 
 
69th percentile
Powered by  Scopus

SCImago Journal & Country Rank

Enter your name and email below to receive latest published articles in Journal of Applied Science and Engineering.