Using the Sagdeev potential method, the existence of large amplitude dust-acoustic solitons andsupersolitons is investigated in a plasma comprising cold negative dust, adiabatic positive dust,Boltzmann electrons, and non-thermal ions. This model supports the existence of positive potentialsupersolitons in a certain region in parameter space in addition to regular solitons having negativeand positive potentials. The lower Mach number limit for supersolitons coincides with theoccurrence of double layers whereas the upper limit is imposed by the constraint that the adiabaticpositive dust number density must remain real valued. The upper Mach number limits for negativepotential (positive potential) solitons coincide with limiting values of the negative (positive)potential for which the negative (positive) dust number density is real valued. Alternatively, theexistence of positive potential solitons can terminate when positive potential double layers occur.
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