Dust-acoustic solitary and periodic waves in a plasma with ion distribution with trapped particles

Abstract

The nonlinear propagation of electrostatic dust-acoustic waves is studied in an unmagnetized three-component dusty plasma consisting of negatively charged dust, free as well as a small percentage of trapped ions and Maxwellian electrons. By using the reductive perturbation technique, a Korteweg de Vries type equation, which governs the dynamics of the small-amplitude solitary and periodic waves of the dusty plasma under consideration, is derived. The traveling soliton (shown to be only of the rarefactive type) and periodic solutions of the KdV type equation are obtained. Bifurcation analysis for the obtained nonlinear KdV type equation is used to describe the qualitative phase portrait for the corresponding dynamical system, which is found to be controlled by the plasma system parameters. The effects of trapped ions and free electrons on the dust-acoustic solitons and periodic waves are discussed. The present investigation may be useful in understanding some nonlinear features of the dust-acoustic waves, which have been observed in astrophysical plasmas such as Saturn's moon Enceladus.

Keywords:

• Dusty plasma
• modified KdV Equation
• bifurcation theory
• solitary acoustic waves
• acoustic periodic waves
• trapped ions

Acknowledgement

The authors also thank the editor and his staff for their kind cooperation.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available within the article.

Additional information

Notes on contributors

M.M. Selim

Mustafa M Selim was born in Damietta, Egypt in 1970. He received a Ph.D. degree in theoretical physics in 2004 from Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Slovakia. He is currently a Professor of Theoretical Physics at Faculty of Science, Damietta University, Egypt. His main research interests are stochastic differential and difference equations and their applications, theoretical plasma physics, solutions of nonlinear equations. . He has published more than 50 papers in international indexed scientific journals. He has also contributed as a Reviewer in many scientific international indexed journals.

H. Abdelaleem

H. Abdelaleem was born in Port Said, Egypt in 1972. He received his B.Sc. degree, Physics in 2012 from Faculty of Science, Port said University, Egypt. Recently, he received a Master degree in Theoretical Physics from Faculty of Science, Damietta University, Egypt in 2022. His main research interests include theoretical plasma physics and Mathematica programming.

N.A. El-Bedwehy

N.A. El-Bedwehy was born in Damietta, Egypt in 1956. She received a Ph.D. degree in Applied Mathematics from the Faculty of Science, Mansoura University, Egypt, in 1992. She is currently an Associated Professor of Applied Mathematics at the Faculty of Science, Damietta University, Egypt. Her main research interests include theoretical plasma physics, nonlinear equations in quantum and classical plasmas and fluids. She has authored more than 40 published papers in international scientific journals on applied mathematics and problems in plasmas. She has also contributed as a Reviewer in some scientific international journals.

E.F. El-Shamy

E. F. El-Shamy was born in Damietta, Egypt in 1971. He received a Ph.D. degree in theoretical plasma physics from the Faculty of Science, Damietta Branch, Mansoura University, Egypt, in 2002. He is currently a Professor of Theoretical Plasma Physics at the Faculty of Science, Damietta University, Egypt. His main research interests include theoretical plasma physics, nonlinear structures in plasmas and fluids, collective processes in space physics, and astrophysics. His present interests involve the physics of degenerate plasmas, wave-wave interaction, and multi-component plasmas. He has authored more than 70 published papers in the best scientific journals on linear and nonlinear waves in plasmas. He has also contributed as a Reviewer in some scientific journals.