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Acoustic supersolitons arise when a plasma model is able to support three consecutive local extrema of the Sagdeev pseudopotential between the undisturbed conditions and an accessible root. This leads to a characteristic electric ﬁeld signature, where a simple bipolar shape is enriched by subsidiary maxima. Large-amplitude nonlinear acoustic modes are investigated, using a pseudopotential approach, for plasmas containing two-temperature electrons having Boltzmann or kappa distributions, in the presence of cold ﬂuid ions. The existence domains for positive supersolitons are derived in a methodological way, both for structure velocities and amplitudes, in terms of plasma compositional parameters. In addition, typical pseudopotentials, soliton, and electric ﬁeld proﬁles have been given to illustrate that positive supersolitons can be found in the whole range of electron distributions from Maxwellian to a very hard nonthermal spectrum in kappa. However, it is found that the parameter ranges that support supersolitons vary signiﬁcantly over the wide range of kappa considered. VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4818888]
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