Ion-acoustic solitons in Bi-Ion dusty plasma

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 compression 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 dust densities around the critical value within which solitary waves with positive and negative potentials can exist simultaneously is relatively wide.