Analytical solutions to (modified) Korteweg–de Vries–Zakharov–Kuznetsov equation and modeling ion-acoustic solitary, periodic, and breather waves in auroral magnetoplasmas

Author:

Alhejaili Weaam1ORCID,Roy Subrata2ORCID,Raut Santanu3ORCID,Roy Ashim4,Salas Alvaro H.5ORCID,Aboelenen Tarek6ORCID,El-Tantawy S. A.7ORCID

Affiliation:

1. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University 1 , P. O. Box 84428, Riyadh 11671, Saudi Arabia

2. Department of Mathematics, Cooch Behar Panchanan Barma University 2 , Cooch Behar 736101, India

3. Department of Mathematics, Mathabhanga College 3 , Cooch Behar 736146, India

4. Department of Mathematics, Alipurduar College 4 , Alipurduar 736122, India

5. Department of Mathematics and Statistics, Universidad Nacional de Colombia, FIZMAKO Research Group 5 , Bogotá 111321, Colombia

6. Department of Mathematics, College of Science, Qassim University 6 , Buraydah 51452, Saudi Arabia

7. Department of Physics, Faculty of Science, Al-Baha University 7 , P.O. Box 1988, Al-Baha, Saudi Arabia

Abstract

This article investigates the propagation of different types of nonlinear ion-acoustic waves, including periodic waves, solitons, and breathers in non-Maxwellian magnetized plasma. The plasma model consists of inertial cold ions, inertialess cold electrons that obey a Boltzmann distribution, and inertialess non-Maxwellian hot electrons that follow the generalized (r, q) distribution. The reductive perturbation technique is utilized to obtain the Korteweg–de Vries–Zakharov–Kuznetsov equation (KdV-ZK) from the fluid equations that govern plasma dynamics. Furthermore, the modified KdV-ZK equation is derived due to the limited capability of the KdV-ZK model to represent the dynamics of the nonlinear structures at specific critical values of the relevant physical variables in the investigated system. The periodic solutions to the two models (KdV-ZK and mKdV-ZK models) are derived using Jacobi elliptic functions. This approach directly links periodic waves (cnoidal waves) and soliton solutions. Hirota's bilinear method generates breathers for both models. Finally, we examine the quantitative understanding of the effects of several physical parameters replicated by the Swedish satellite Viking incorporated in the model. The findings reported in this study enhance our comprehension of the properties of the electron distribution function's high- and low-energy segments and the development of periodic, soliton, multi-soliton, and breather phenomena in space and astrophysical plasmas.

Funder

Deanship of Scientific Research, Princess Nourah Bint Abdulrahman University

Publisher

AIP Publishing

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