article · International Journal of Numerical Methods for Heat & Fluid Flow
This research provides an analytical investigation into nonplanar dust-acoustic solitary and cnoidal waves within the dusty plasma of the lunar terminator region. Using a three-component fluid plasma model that accounts for inertial negatively charged dust and Boltzmann electrons and ions, the system is reduced to nonplanar Korteweg-de Vries equations in both standard integer and time-fractional forms. The mathematical models examine cylindrical and spherical geometries alongside temporal memory effects. Results demonstrate that only rarefactive wave structures form under lunar terminator conditions. Geometric curvature introduces explicit time dependence, leading to reduced wave amplitudes and changing widths over time, with spherical geometries demonstrating stronger effects than cylindrical forms. Furthermore, higher dust concentration and elevated electron-to-ion temperature ratios decrease wave amplitude and width.
Dust dynamics in the lunar environment influence electrostatic activity and particulate transport near the Moon's surface. Understanding how plasma waves behave in curved space and over time helps scientists model the physical environment of the lunar terminator. This provides foundational theoretical benchmarks needed to interpret data from numerical space simulations and upcoming lunar exploration missions.
This is early-stage theoretical and mathematical research without direct commercial applications. The analytical models may eventually assist aerospace agencies, mission planners, and scientific software developers in designing numerical simulations and interpreting in situ electrostatic measurements collected by lunar instruments. However, the abstract does not indicate any current commercialisation pathway or direct industry partnership.
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Purpose This work aims to investigate, for the first time, the nonplanar (cylindrical and spherical geometries) integer and time-fractional dust-acoustic (DA) solitary and cnoidal waves (CWs) in the lunar terminator dusty plasma, focusing on the combined influence of geometric curvature and temporal memory. Design/methodology/approach A three-component fluid plasma model with inertial negatively charged dust and Boltzmann electrons and ions is considered under nonplanar geometries. The reductive perturbation technique reduces the fluid model to a nonplanar Korteweg-de Vries (KdV) equation, for which a time-dependent ansatz provides semi-analytical solitary and CW solutions. Replacing the first-order time derivative with the fractional Caputo derivative yields a nonplanar fractional KdV equation, which is solved using the Tantawy technique. Findings For parameters relevant to the lunar terminator, only rarefactive DA structures are supported. Curvature makes solitary and CWs explicitly time-dependent, with amplitudes decreasing and widths evolving during propagation, and spherical waves are more strongly affected than cylindrical ones. Higher dust concentration and electron-to-ion temperature ratio reduce the amplitude and width, while decreasing a further dampens the structures; the semi-analytical solutions remain accurate according to residual-error measures. Practical implications The nonplanar integer and fractional KdV models supply a compact framework for interpreting nonlinear electrostatic activity and dust transport in the lunar terminator region and can serve as benchmarks for numerical simulations and future in situ observations. Originality/value To the best of the authors’ knowledge, this study provides the first analytical treatment of cylindrical and spherical DA solitary and CWs within a time-fractional KdV formulation tailored to the lunar terminator plasma and demonstrates a combined ansatz-Tantawy approach for nonintegrable curvature-modified fractional evolution equations.
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DOI: 10.1108/hff-05-2026-0684
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