<p>In this study, the impact of multiple noise on the stochastic coupled equations of sound waves with Langmuir waves in the Itô sense is examined. This model investigates the Langmuir collapsing wave, a nonlinear phenomena that offers valuable scientific information on powerful Langmuir turbulences, the Langmuir observations of the solar radio explosion, and the explanation of unknown subsonic and supersonic limits of behavior in the turbulences. Since the plasma substances are intrinsically random and unpredictable, the incorporation of noise effects is crucial to the proper captioning of the energy flow and localization processes. Novel stochastic solutions including periodic, quasi-periodic, internal envelope, compacton, parabolic, dark and bright soliton solutions of the ion sound and Langmuir waves coupled stochastic equations are obtained with the help of the <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>k</mi> <mo>+</mo> <mfrac> <msup> <mi>G</mi> <mo>′</mo> </msup> <mi>G</mi> </mfrac> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(k+\frac{G'}{G} )$</EquationSource> </InlineEquation>-expansion method. The proposed ansatze converts the targeted model into a nonlinear ordinary differential equation (NODE) using a sophisticated structured wave transformation. By supposing the closed form solution, a nonlinear algebraic system is further built from the resulting NODE. Analytically solving the resultant algebraic system with symbolic computation tool Maple yields a new range of explicit solutions in the form of rational, trigonometric and hyperbolic functions. By using the novel <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>k</mi> <mo>+</mo> <mfrac> <msup> <mi>G</mi> <mo>′</mo> </msup> <mi>G</mi> </mfrac> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(k+\frac{G'}{G} )$</EquationSource> </InlineEquation>-expansion approach to the stochastic plasma model for the first time, the research study offers a new scientific explanation of the nonlinear behavior of Langmuir and ion sound waves when subjected to the effects of noise.</p>

Noise effect on plasma solitons in the realm of ion sound and Langmuir waves stochastic coupled equations

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2026年3月10日

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Fatemah Mofarreh

摘要

In this study, the impact of multiple noise on the stochastic coupled equations of sound waves with Langmuir waves in the Itô sense is examined. This model investigates the Langmuir collapsing wave, a nonlinear phenomena that offers valuable scientific information on powerful Langmuir turbulences, the Langmuir observations of the solar radio explosion, and the explanation of unknown subsonic and supersonic limits of behavior in the turbulences. Since the plasma substances are intrinsically random and unpredictable, the incorporation of noise effects is crucial to the proper captioning of the energy flow and localization processes. Novel stochastic solutions including periodic, quasi-periodic, internal envelope, compacton, parabolic, dark and bright soliton solutions of the ion sound and Langmuir waves coupled stochastic equations are obtained with the help of the $(k + \frac{G^{'}}{G})$ $(k+\frac{G'}{G} )$ -expansion method. The proposed ansatze converts the targeted model into a nonlinear ordinary differential equation (NODE) using a sophisticated structured wave transformation. By supposing the closed form solution, a nonlinear algebraic system is further built from the resulting NODE. Analytically solving the resultant algebraic system with symbolic computation tool Maple yields a new range of explicit solutions in the form of rational, trigonometric and hyperbolic functions. By using the novel $(k + \frac{G^{'}}{G})$ $(k+\frac{G'}{G} )$ -expansion approach to the stochastic plasma model for the first time, the research study offers a new scientific explanation of the nonlinear behavior of Langmuir and ion sound waves when subjected to the effects of noise.