Numerical Analysis of Nonlinear Electron Acoustic Lump Solitons in a Homogeneous, Unmagnetized, Collision less Plasma

Electron-acoustic waves in a homogeneous, unmagnetized, collisionless plasma composed ofinertial cold electrons, κ-distributed hot electrons, and stationary ions are investigated. Starting from the fluid equations coupled with Poisson’s equation, the reductive perturbation method is systematically applied with appropriate stretched coordinates to derive a two-dimensional Kadomtsev–Petviashvili (KP) equation governing the weakly nonlinear evolution of electron-acoustic perturbations, including weak transverse effects. The nonlinear and dispersive coefficients of the KP equation are obtained explicitly in terms of the plasma density ratio and the superthermality index κ. Exact lump soliton solutions are then constructed using a rational-function approach, yielding fully localized two-dimensional structures that decay algebraically in space. Parametric analysis shows that κ significantly influences the amplitude and localization of the lump solitons; lower κ values enhance nonlinearity and produce higher, more localized structures, whereas larger κ leads to broader and weaker excitations. These results clarify the role of super thermal electrons in multidimensional nonlinear wave dynamics.