Acta Scientific Computer Sciences

Review Article Volume 5 Issue 1

Analytic Solutions to the System of Ion Sound and Langmuir Waves Via First Integral Method

Ammar Al-Salih*

Directorate of Education in Basra, Basrah, Iraq

*Corresponding Author: Ammar Al-Salih, Directorate of Education in Basra, Basrah, Iraq.

Received: August 16, 2022; Published: December 12, 2022

Abstract

The goal of this paper is to look into a nonlinear system of partial differential equations (PDEs) with unknown functions that are both complex and real-valued. We use the first integral method based on commutative algebra theory to construct new solutions to the system of ion sound and Langmuir waves. All algebraic computations in this work are performed using the Maple software. This method is significant, efficient, and applicable to a diverse set of nonlinear differential equations.

Keywords: The System of Ion Sound and Langmuir Waves; First Integral Method; Traveling Wave Solutions; Commutative Algebra; Nonlinear Partial Differential Equations

References

  1. Abdou M. “Exact Travelling Wave Solutions in a Nonlinear Elastic Rod Equation”. International Journal of Nonlinear Science2 (2009): 167-173.
  2. Alaidarous E. “F-Expansion method for the nonlinear generalized Ito System”. International Journal of Basic and Applied Sciences2 90-117.
  3. Alquran M., et al. “Applications of First Integral Method to Some Complex Nonlinear Evolution Systems”. Applied Mathematics and Information Sciences2 (2015): 825-831.
  4. Al-Salih A. “New Exact Travelling Wave Solutions for Some Nonlinear Partial Differential Equations by Using Tanh Method”. Australian Journal of Basic and Applied Sciences8 (2016): 114-118.
  5. Arbabi S and Najafi M. “New Periodic and Soliton Solutions of (2 + 1)-Dimensional Soliton Equation”. Journal of Advanced Computer Science and Technology4 (2012): 232-239.
  6. Aslan I. “Exact and explicit solutions to some nonlinear evolution equations by utilizing the (G'/G)-expansion method”. Applied Mathematics and Computation 215 (2009): 857-863.
  7. Borhanifar A and Moghanlu A. “Application of the (G'/G )-expansion method for the Zhiber-Shabat equation and other related equations”. Mathematical and Computer Modelling 54 (2011): 2109-2116.
  8. Feng Z. “On explicit exact solutions to the compound Burgers-KdV equation”. Physics Letters A 293 (2002): 57-66.
  9. Feng Z and Wang X. “The first integral method to the two-dimensional Burgers-Korteweg-de Vries equation”. Physics Letters A 308 (2003): 173-178.
  10. Filiz A., et al. “𝐹-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation”. Scientific World Journal (2014): 1-14.
  11. Hassan S and Abdelrahman M. “A Riccati-Bernoulli sub-ODE Method for Some Nonlinear Evolution Equations”. IJNSNS (2019): 1-11.
  12. Hosseini K., et al. “Exact solutions of some nonlinear systems of partial differential equations by using the first integral method”. Journal of Mathematical Analysis and Applications 387 (2012): 807-814.
  13. Hosseini M., et al. “Exact travelling solutions for the sixth-order Boussinesq equation”. The Journal of Mathematics and Computer Science2 (2011): 376-387.
  14. Jafari H and Kadkhoda N. “Application of simplest equation method to the (2+1)-dimensional nonlinear evolution equations”. New Trends in Mathematical Sciences (2014): 64-68.
  15. Muhammad-Jawad A. “Tanh Method for Solutions of Non-linear Evolution Equations”. Journal of Basrah Researches4 (2011).
  16. Peng Y and Krishnan E. “Exact Travelling Wave Solutions for a Class of Nonlinear Partial Differential Equations”. International Journal of Pure and Applied Mathematical Sciences 1 (2006): 11-20.
  17. Taghizadeh N., et al. “The first-integral method applied to the Eckhaus equation”. Applied Mathematics Letters 25 (2012): 798-802.
  18. Tajadodi H., et al. “Exact solutions of conformable fractional differential equations”. Results in Physics 22 (2021).
  19. Ugurlu Y., et al. “Traveling Wave Solutions of the RLW and Boussinesq Equations”. New Trends in Mathematical Sciences (2014): 69-77.
  20. Xue-qin Z., et al. “Constructing Exact Solutions for Two Nonlinear Systems”. 28.1 (2008): 111-118.
  21. Zakharov V. “Collapse of Langmuir Waves”. Soviet Physics Jetp5 (1972): 908-914.

Citation

Citation: Ammar Al-Salih. “Analytic Solutions to the System of Ion Sound and Langmuir Waves Via First Integral Method".Acta Scientific Computer Sciences 5.1 (2023): 63-66.

Copyright

Copyright: © 2023 Ammar Al-Salih. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.




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Acceptance rate35%
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