Memory-modified ion-acoustic solitary waves in κ-distributed plasmas: from Hirota benchmarks to fractional KdV-KP dynamics

Abstract Ion-acoustic solitary waves offer a useful test bed for separating plasma nonthermality from memory effects. Starting from a cold-ion fluid model with suprathermal κ-distributed electrons, we derive the κ-dependent Kortewegde Vries (KdV) and Kadomtsev-Petviashvili (KP) coefficients by reductive perturbation theory. A Caputo derivative of order 0 < α ≤ 1 is introduced only afterwards as a phenomenological slow-time memory closure, so the roles of κ and α remain distinct. At α = 1, the classical KdV equation is integrable and exact Hirota one-and two-soliton solutions provide demanding benchmarks for the numerical solver. For α < 1, we evolve the fractional KdV and KP-II equations directly with an L1-Fourier pseudospectral scheme, without assuming a fractional soliton form. The implementation reproduces secondorder convergence in the classical limit, keeps KdV invariant drifts below 1.1 × 10 -4 , and passes fractional time-step and KP spatial-resolution checks. The simulations show that stronger memory reduces crest speed and peak amplitude and postpones overtaking interactions for every tested κ. In KP-II, it also produces a small additional decrease in a weak transverse displacement modulation over the simulated interval, together with longitudinal reshaping. These results identify a measurable departure from integrable ion-acoustic dynamics while keeping suprathermal statistics and temporal memory as separate modeling controls.