  The propagation of ion-acoustic solitons in a warm dusty plasma containing
two ion species is investigated theoretically. Using an approach based on the
Korteveg-de-Vries equation, it is shown that the critical value of the negative
ion density that separates the domains of existence of compressi- on and
rarefaction solitons depends continuously on the dust density. A modified
Korteveg-de Vries equation for the critical density is derived in the higher
order of the expansion in the small parameter. It is found that the nonlinear
coefficient of this equation is positive for any values of the dust density and
the masses of positive and negative ions. For the case where the negative ion
density is close to its critical value, a soliton solution is found that takes
into account both the quadratic and cubic nonlinearities. The propagation of a
solitary wave of arbitrary amplitude is investigated by the quasi-potential
method. It is shown that the range of the dust densities around the critical
value within which solitary waves with positive and negative potentials can
exist simultaneously is relatively wide.
