Eur. Phys. J. Plus (2021) 136: 1075
https://doi.org/10.1140/epjp/s13360-021-02087-3

Regular Article

Exponential time differencing method for modeling the dissipative rouge waves and breathers in a collisional plasma

¹ Department of Mathematics, Faculty of Sciences and Arts-Rabigh Campus, King Abdulaziz University, Jeddah, Saudi Arabia
² Department of Physics, Faculty of Science, Port Said University, 42521, Port Said, Egypt
³ Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al- Mikhwah, Al-Baha University, Al-Baha, Saudi Arabia
⁴ Mathematics Department, Faculty of Science, Al-Sulymania Women’s Campus, King Abdulaziz University, P.O. Box 80200, 21589, Jeddah, Saudi Arabia
⁵ Department of Mathematics, Saint Xavier University, 60655, Chicago, IL, USA

^a Nhaljahdaly@kau.edu.sa

Received: 24 August 2021
Accepted: 19 October 2021
Published online: 27 October 2021

Abstract

We employ numerical methods to investigate the dissipative freak waves (FWs) and dissipative breathers (Bs) in collisional electronegative complex plasmas. The plasmas under investigation possess inertialess Maxwellian thermal electron and light negative ion in addition to stationary negatively charged dust grains. To achieve this goal, we reduce the fluid equation of the plasma species to the linear damped nonlinear Schrödinger equation (NLSE) via using the derivative expansion technique. The modulational instability (MI) is investigated and the (un)stable regions are determined precisely in order to study the dynamic of mechanism of the dissipative modulated structures. To study the effect of related plasma parameters on the behavior of the dissipative FWs and Bs, the linear damped NLSE is solved numerically using exponential time differencing method. In addition, the relative error is estimated to prove the accuracy of the proposed method. The impact of the plasma configuration parameters on the regions of the (un)stable envelope structures is discussed. Moreover, the dependence of the dissipative FWs and dissipative Bs profiles on the plasma configuration parameters is examined and reported.