Nonplanar Solitons in Plasma With Cairns–Gurevich Electrons via Weighted Residual Method

We investigate the formation and evolution of nonlinear electrostatic structures in a collisionless, unmagnetized plasma comprising Cairns-Gurevich distributed electrons, accounting for both energetic populations and trapped particles. Utilizing the reductive perturbation technique (RPT), a nonplanar Schamel-type evolution equation is derived and analytically solved via the weighted residual method (WRM). To validate and extend the analytical insights, numerical simulations are performed in planar, cylindrical, and spherical geometries using the newly developed FORKET simulation code. The study also incorporates real-space observational data from the MMS-1 spacecraft on 2 November 2024, where precise ephemeris information facilitated modeling of plasma dynamics in the outer magnetosphere under realistic conditions. The spatiotemporal behavior of solitons is analyzed in relation to physical parameters such as the nonthermal and trapping factors, as well as initial wave speeds. The results demonstrate significant differences in soliton profiles between planar and nonplanar geometries, with important implications for understanding plasma behavior in both space environments and laboratory settings where electron trapping is significant.