A Self-Consistent Model of Kinetic Alfven Solitons in Pulsar Wind Plasma: Linking Soliton Characteristics to Pulsar Observables

A self-consistent model is presented for the formation and propagation of kinetic Alfv\'en (KA) solitons in mass-loaded filaments within the pulsar wind, where a magnetized electron--positron--ion plasma flows along open magnetic field lines beyond the light cylinder. Using a reductive perturbation approach, we derive a Korteweg--de Vries (KdV) equation governing the nonlinear evolution of KA solitons in this environment. The soliton amplitude and width depend sensitively on key pulsar observables, including spin period, spin-down rate, and pair multiplicity, as well as on plasma composition and suprathermal particle distributions. Heavy ion species such as Fe$^{26+}$ produce significantly broader solitons through enhanced inertia and dispersion, while increasing pair multiplicity leads to smaller solitons through stronger screening. More oblique propagation (larger $\theta$) yields wider but lower-amplitude solitons, whereas more thermalized pair plasmas (higher $\kappa$) support taller and broader structures. A population-level analysis of 1174 pulsars quantifies the physical scales of these nonlinear structures, showing that millisecond pulsars host the most compact solitons, whereas slower pulsars support broader structures. Within the adopted admissible finite-$\beta$ regime, this work links soliton properties to measurable pulsar parameters and provides a self-consistent framework for characterizing localized nonlinear plasma structures in finite-magnetization regions of pulsar winds and for assessing their role in modulating the local plasma environment.