Electron holes in a <i>κ</i> distribution background with singularities

The pseudo-potential method is applied to derive diverse propagating electron hole structures, in a nonthermal or $\kappa$ particle distribution function background. associated Ansatz reproduces the Schamel of \cite{Schamel2015} Maxwellian ($\kappa \rightarrow \infty$) limit, providing significant generalization it for plasmas where superthermal electrons are ubiquitous, such as space plasmas. and nonlinear dispersion relation evaluated. role spectral index on investigated, what concerns wave amplitude instance. energy-like first integral from Poisson's equation analyze properties classes solutions: with absence trapped electrons, non-analytic surplus electrons. Special attention therefore paid non-orthodox case exhibits strong singularities, being discontinuous non-analytic.