Nonplanar integer and fractional dust-acoustic solitary and cnoidal waves in lunar terminator plasma: a first analytical investigation

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.