Soliton solutions for system of ion sound and Langmuir waves
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Soliton solutions for system of ion sound and Langmuir waves Wael W. Mohammed1,3 · Mahmoud A. E. Abdelrahman2,3 · Mustafa Inc4,5 · A. E. Hamza1 · Mehmet Ali Akinlar6 Received: 22 March 2020 / Accepted: 3 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We study on constructing new traveling wave solution of a system known as ion sound and Langmuir waves by using method of extended Jacobian elliptic function expansion and He’s semi-inverse technique. Some new solutions will be beneficial for researchers concerning with nonlinear physical phenomena. The proposed methods may serve as the framework for solutions of various equations in applied science. Graphical simulations are provided to illustrate the behavior of these solutions. Keywords Elliptic functions · Variational principles · Ion sound and Langmuir waves · Nonlinear physical phenomena · Dark and bright solitons · Traveling wave solutions
* Mustafa Inc [email protected] Wael W. Mohammed [email protected] Mahmoud A. E. Abdelrahman [email protected] A. E. Hamza [email protected] Mehmet Ali Akinlar [email protected] 1
Department of Mathematics, Faculty of Science, University of Ha’il, Hail, Saudi Arabia
2
Department of Mathematics, College of Science, Taibah University, Al‑Madinah Al‑Munawarah, Saudi Arabia
3
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
4
Department of Mathematics, Faculty of Science, Firat University, 23119 Elazig, Turkey
5
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
6
Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey
13
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1 Introduction The field of nonlinear PDEs is a branch of science by means of which many different scientific and engineering phenomena are efficiently modeled. Some research work regarding modeling, solutions and applications of PDEs may be seen in, e.g. Abdelrahman and Kunik (2015), Abdelrahman (2017a, b, 2018), Razborova et al. (2014), Biswas and Mirzazadeh (2014), Younis et al. (2015), Bhrawy (2014) and Abdelrahman and Sohaly (2017, 2018). Methods of expfunction (He and Wu 2006; Aminikhad et al. 2009), tanh–sech (Malfliet and Hereman 1996; Wazwaz 2004a), sine–cosine (Wazwaz 2004b, 2005), F-expansion (Zhang et al. 2006; Ren and Zhang 2006), Jacobi elliptic function (Dai and Zhang 2006; Fan and Zhang 2002), extended tanh (EL-Wakil and Abdou 2007; Wazwaz 2007), perturbation ( method ) (Mohammed ′ 2018, 2020), homogeneous balance (Fan and Zhang 1998; Wang 1996), GG -expansion (Dai
and Zhang 2006; Fan and Zhang 2002), Riccati–Bernoulli sub-ODE (Abdelrahman and Sohaly 2017; Yang et al. 2015). Recently, there are great development in analytical methods for finding solutions for NPDEs, see for example Rizvi et al. (2020a, b), Ali et al. (2020), Younis et al. (2020), Goswami et al. (2018, 2019a, b), Dubey et al. (2020) and Veer
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