This study explores the properties and bifurcation dynamics of ion-acoustic waves in a collisionless plasma with nonextensive-trapped electrons, employing a Tsallis–Gurevich distribution to model both free and trapped electron populations. We demonstrate that the nonextensivity parameter q critically influences soliton characteristics, with increasing q leading to reduced phase velocity, enhanced amplitude, and narrower pulse width in both super-extensive (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$q < 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>) and sub-extensive (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$q > 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>) regimes. Energy analysis reveals a dual dependence on q, decreasing in super-extensive conditions but increasing in sub-extensive cases, highlighting the role of nonextensive statistics in soliton energetics. In addition, trapped-ion correlations exhibit an inverse relationship with bipolar field strength, where weaker interactions yield more intense localized electric fields. Through phase space analysis of the modified Korteweg–de Vries (mK-dV) equation, we identify distinct nonlinear wave regimes governed by the nonextensivity index q. For super-extensive plasmas (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$q < 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>), the trajectories form closed, bounded loops in the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$(\Phi , z)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Φ</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> plane, corresponding to stable oscillatory or cnoidal-type solutions. As q decreases, these loops enlarge and become increasingly distorted, indicating enhanced nonlinearity and higher soliton amplitudes driven by superthermal electrons. Conversely, in the sub-extensive regime (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$q > 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>), the phase trajectories become open and unbounded, signifying nonperiodic or weakly nonlinear dispersive structures rather than localized solitons. These results demonstrate that electron nonextensivity controls the transition from coherent solitary waves to complex, nonperiodic structures, providing a unified framework for understanding nonlinear wave dynamics in space and astrophysical plasmas.

From solitons to complex structures: how nonextensive-trapped electrons transform ion-acoustic waves in plasmas

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发表日期：

2026年1月1日

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N. Bouchemla,
A. Merriche,
R. Fermous,
M. Benzekka

摘要

This study explores the properties and bifurcation dynamics of ion-acoustic waves in a collisionless plasma with nonextensive-trapped electrons, employing a Tsallis–Gurevich distribution to model both free and trapped electron populations. We demonstrate that the nonextensivity parameter q critically influences soliton characteristics, with increasing q leading to reduced phase velocity, enhanced amplitude, and narrower pulse width in both super-extensive ( $q < 1$ $q < 1$ ) and sub-extensive ( $q > 1$ $q > 1$ ) regimes. Energy analysis reveals a dual dependence on q, decreasing in super-extensive conditions but increasing in sub-extensive cases, highlighting the role of nonextensive statistics in soliton energetics. In addition, trapped-ion correlations exhibit an inverse relationship with bipolar field strength, where weaker interactions yield more intense localized electric fields. Through phase space analysis of the modified Korteweg–de Vries (mK-dV) equation, we identify distinct nonlinear wave regimes governed by the nonextensivity index q. For super-extensive plasmas ( $q < 1$ $q < 1$ ), the trajectories form closed, bounded loops in the $(\Phi , z)$ $(Φ, z)$ plane, corresponding to stable oscillatory or cnoidal-type solutions. As q decreases, these loops enlarge and become increasingly distorted, indicating enhanced nonlinearity and higher soliton amplitudes driven by superthermal electrons. Conversely, in the sub-extensive regime ( $q > 1$ $q > 1$ ), the phase trajectories become open and unbounded, signifying nonperiodic or weakly nonlinear dispersive structures rather than localized solitons. These results demonstrate that electron nonextensivity controls the transition from coherent solitary waves to complex, nonperiodic structures, providing a unified framework for understanding nonlinear wave dynamics in space and astrophysical plasmas.