<p>This study is focused on the nonlinear analysis of dust acoustic waves (DAWs) in a viscous plasma impacted by weakly relativistic semi-classical electrons, positrons, and dust particles. A system of fluid equations that includes the kinematic viscosity impact on the inertial dust grain component is used to obtain the nonlinear evolution equations. Chandrasekhar’s equation of state is considered to reflect the semi-classical state of electrons and positrons. The Korteweg–de Vries–Burger (KdV-B) equation is derived using the Krylov–Bogoliubov–Mitropolsky (KBM) perturbation method for long-wavelength approximation, and the influence of kinematic viscosity on the shock or double layer soliton is portrayed. For the first time, the KBM approach is used to construct the KdV-B equation for the plasma system in place of the traditional reductive perturbation method. Also, the complex nonlinear Schrödinger equation (CNLSE) for the regime of small wavelength is derived using the aforementioned framework. Later, the stability of this plasma system is explored by performing the modulation instability and bifurcation analysis. Numerical results reveal that plasma factors, such as dust charge number (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41614_2025_183_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$Z_d$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>Z</mi> <mi>d</mi> </msub> </math></EquationSource> </InlineEquation>), viscosity (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41614_2025_183_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\eta$</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>), and dust density (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41614_2025_183_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$n_{d0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>n</mi> <mrow> <mi>d</mi> <mn>0</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>), substantially impact the shock structures, rogons, and the modulation instability conditions. This study aims to elucidate the electron–positron plasma system within an astrophysical context like out-spills of Black Holes, Active Galactic Nuclei, Gamma-ray Bursts, and Pulsar Wind Nebulae. Results of the present theoretical study can be verified using laboratory setups with some instrumental modifications of previously performed experimental studies.</p>

Stationary structures and stability analysis of dust acoustic waves in dense stellar environment

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发表日期：

2025年2月21日

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Jit Sarkar,
Shatadru Chaudhuri,
A. Roy Chowdhury,
Asit Saha

摘要

This study is focused on the nonlinear analysis of dust acoustic waves (DAWs) in a viscous plasma impacted by weakly relativistic semi-classical electrons, positrons, and dust particles. A system of fluid equations that includes the kinematic viscosity impact on the inertial dust grain component is used to obtain the nonlinear evolution equations. Chandrasekhar’s equation of state is considered to reflect the semi-classical state of electrons and positrons. The Korteweg–de Vries–Burger (KdV-B) equation is derived using the Krylov–Bogoliubov–Mitropolsky (KBM) perturbation method for long-wavelength approximation, and the influence of kinematic viscosity on the shock or double layer soliton is portrayed. For the first time, the KBM approach is used to construct the KdV-B equation for the plasma system in place of the traditional reductive perturbation method. Also, the complex nonlinear Schrödinger equation (CNLSE) for the regime of small wavelength is derived using the aforementioned framework. Later, the stability of this plasma system is explored by performing the modulation instability and bifurcation analysis. Numerical results reveal that plasma factors, such as dust charge number ( $Z_d$ $Z_{d}$ ), viscosity ( $\eta$ $η$ ), and dust density ( $n_{d0}$ $n_{d 0}$ ), substantially impact the shock structures, rogons, and the modulation instability conditions. This study aims to elucidate the electron–positron plasma system within an astrophysical context like out-spills of Black Holes, Active Galactic Nuclei, Gamma-ray Bursts, and Pulsar Wind Nebulae. Results of the present theoretical study can be verified using laboratory setups with some instrumental modifications of previously performed experimental studies.