A comparison of analytical solutions of nonlinear complex generalized Zakharov dynamical system for various definitions of the differential operator

Melih Cinar; Ismail Onder; Aydin Secer; Mustafa Bayram; Abdullahi Yusuf; Tukur Abdulkadir Sulaiman; Melih Cinar; Ismail Onder; Aydin Secer; Mustafa Bayram; Abdullahi Yusuf; Tukur Abdulkadir Sulaiman

doi:10.3934/era.2022018

Electronic Research Archive

2022, Volume 30, Issue 1: 335-361. doi: 10.3934/era.2022018

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Research article

A comparison of analytical solutions of nonlinear complex generalized Zakharov dynamical system for various definitions of the differential operator

1.
Department of Mathematical Engineering, Yildiz Technical University, Istanbul, TURKEY
2.
Graduate School of Science and Engineering, Yildiz Technical University, Istanbul, TURKEY
3.
Department of Computer Engineering, Biruni University, Istanbul, TURKEY
4.
Department of Mathematics, Federal University Dutse, Jigawa, NIGERIA

Academic Editor: Alain Miranville

Received: 21 October 2021 Revised: 02 December 2021 Accepted: 23 December 2021 Published: 13 January 2022

This paper considers deriving new exact solutions of a nonlinear complex generalized Zakharov dynamical system for two different definitions of derivative operators called conformable and $ M- $ truncated. The system models the spread of the Langmuir waves in ionized plasma. The extended rational $ sine-cosine $ and $ sinh-cosh $ methods are used to solve the considered system. The paper also includes a comparison between the solutions of the models containing separately conformable and $ M- $ truncated derivatives. The solutions are compared in the $ 2D $ and $ 3D $ graphics. All computations and representations of the solutions are fulfilled with the help of Mathematica 12. The methods are efficient and easily computable, so they can be applied to get exact solutions of non-linear PDEs (or PDE systems) with the different types of derivatives.
- Zakharov dynamical system,
- extended rational sine-cosine method,
- extended rational sinh-cosh method exact solutions
Citation: Melih Cinar, Ismail Onder, Aydin Secer, Mustafa Bayram, Abdullahi Yusuf, Tukur Abdulkadir Sulaiman. A comparison of analytical solutions of nonlinear complex generalized Zakharov dynamical system for various definitions of the differential operator[J]. Electronic Research Archive, 2022, 30(1): 335-361. doi: 10.3934/era.2022018

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Abstract

This paper considers deriving new exact solutions of a nonlinear complex generalized Zakharov dynamical system for two different definitions of derivative operators called conformable and $ M- $ truncated. The system models the spread of the Langmuir waves in ionized plasma. The extended rational $ sine-cosine $ and $ sinh-cosh $ methods are used to solve the considered system. The paper also includes a comparison between the solutions of the models containing separately conformable and $ M- $ truncated derivatives. The solutions are compared in the $ 2D $ and $ 3D $ graphics. All computations and representations of the solutions are fulfilled with the help of Mathematica 12. The methods are efficient and easily computable, so they can be applied to get exact solutions of non-linear PDEs (or PDE systems) with the different types of derivatives.

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