The novel stochastic solutions for ion sound and Langmuir waves model in plasma physics

Mohammed Alharthi; Mohammed Alharthi

doi:10.3934/math.2025713

AIMS Mathematics

2025, Volume 10, Issue 7: 15912-15928. doi: 10.3934/math.2025713

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Research article

The novel stochastic solutions for ion sound and Langmuir waves model in plasma physics

Mohammed Alharthi ^,

Department of Mathematics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia

Received: 19 March 2025 Revised: 23 June 2025 Accepted: 25 June 2025 Published: 15 July 2025
MSC : 35C07, 35Q60, 60H15, 60H40, 82D10

This paper analyzes and examines the ion sound and Langmuir waves (ISALWs) model with noise term utilizing the powerful extended tanh technique and the complete discrimination system for the polynomial method. Namely, we introduce some new stochastic solutions for the ISALWs model with multiplicative noise in the Itô sense. Ion sound waves and Langmuir waves are distinguished as fundamental plasma waves, characterized by varying frequencies, wavelengths, and modes of propagation. The combination of ion inertia and electron pressure results in the propagation of low-frequency electrostatic waves, referred to as ion sound waves, within a plasma. Langmuir waves refer to the high-frequency electrostatic oscillations of electrons within a plasma, while ions, due to their larger mass, are considered to be almost at rest. We also investigate how the noise term affects the structural characteristics of waves. These results have potential relevance to plasma physics applications, such as solar wind dynamics, Langmuir turbulence, and burst-like wave phenomena in cusp regions. Utilizing the capabilities of the MATLAB release, several profile pictures are created to demonstrate the behavior of the presented stochastic solutions. Ultimately, the suggested methodology has the potential to be adapted for various other models in the applied science.
- ISALWs model,
- extended tanh technique,
- complete discrimination system,
- stochastic solutions,
- wave propagation,
- plasma physics
Citation: Mohammed Alharthi. The novel stochastic solutions for ion sound and Langmuir waves model in plasma physics[J]. AIMS Mathematics, 2025, 10(7): 15912-15928. doi: 10.3934/math.2025713

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Abstract

This paper analyzes and examines the ion sound and Langmuir waves (ISALWs) model with noise term utilizing the powerful extended tanh technique and the complete discrimination system for the polynomial method. Namely, we introduce some new stochastic solutions for the ISALWs model with multiplicative noise in the Itô sense. Ion sound waves and Langmuir waves are distinguished as fundamental plasma waves, characterized by varying frequencies, wavelengths, and modes of propagation. The combination of ion inertia and electron pressure results in the propagation of low-frequency electrostatic waves, referred to as ion sound waves, within a plasma. Langmuir waves refer to the high-frequency electrostatic oscillations of electrons within a plasma, while ions, due to their larger mass, are considered to be almost at rest. We also investigate how the noise term affects the structural characteristics of waves. These results have potential relevance to plasma physics applications, such as solar wind dynamics, Langmuir turbulence, and burst-like wave phenomena in cusp regions. Utilizing the capabilities of the MATLAB release, several profile pictures are created to demonstrate the behavior of the presented stochastic solutions. Ultimately, the suggested methodology has the potential to be adapted for various other models in the applied science.

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