Dissipative integer and fractional ion-acoustic solitary waves in non-Maxwellian plasmas are commonly modeled by Korteweg-de Vries (KdV)-type equations, yet collisional damping, electron trapping, and fractional-order memory have so far been treated separately, leaving their combined effect on wave propagation largely unexamined. Because the resulting damped Schamel-KdV equation is non-integrable even at integer order, no closed-form solution exists, and this work aims to construct and validate semi-analytical approximations for both its integer- and time-fractional forms.
Starting from a one-dimensional fluid description with inertial ions, Maxwellian positrons, and non-Maxwellian Schamel electrons, the reductive perturbation technique is used to derive a planar damped Schamel-KdV equation with fractal nonlinearity, together with its time-fractional Caputo counterpart. The integer-order model is treated by tailored ansatz formulations, while the fractional model is analyzed via the Tantawy technique (TT), implemented through two algorithms designed to handle the Schamel-type nonlinearity and the stiff fractional dynamics.
The constructed semi-analytical solutions reproduce, with high accuracy, the amplitude decay, broadening, and polarity behavior of the dissipative solitons under collisional damping and memory effects. Absolute and global maximum residual errors confirm that the Tantawy technique (TT) yields accurate, low-cost fractional approximations with clear dependence on the plasma and fractional parameters, and the residual-error comparison identifies which integer-order ansatz correctly reproduces the expected amplitude decay among several competing candidates. The fractional order is shown to act as an additional control parameter governing the propagation of dissipative Schamel-KdV solitons in regimes beyond the reach of classical integer-order models.
The proposed formulation offers a compact, adaptable framework for modeling dissipative electrostatic structures in multicomponent space and laboratory plasmas with trapped electrons, collisional damping, and nonlocal memory, and the combined ansatz-Tantawy methodology can be extended to other damped KdV-type equations in fluid and thermal transport problems where non-Maxwellian statistics and fractional effects are relevant.
This is the first formulation and analysis of a damped time-fractional Schamel-KdV equation for non-Maxwellian electron-positron-ion plasmas and the first application of the TT to a stiff, dissipative, Schamel-type model. The study shows that Schamel-type nonlinearity, collisional damping, and fractional-order memory can be captured within a single semi-analytical framework, extending the range of dissipative solitary-wave configurations tractable without exclusive recourse to numerical simulation.
