Solutions of generalized constrained discrete KP hierarchy

Solutions of a generalized constrained discrete KP (gcdKP) hierarchy with constraint on Lax operator Lᵏ=(Lᵏ)≥ m+∑ᵢ₌₁ˡqᵢΔ⁻¹Λᵐrᵢ, are invesitigated by Darboux transformations TD(f)=f[1]·Δ· f⁻¹ and TI(g)=(g[-1])⁻¹·Δ⁻¹· g. Due to this special constraint on Lax operator, it is showed that the generating functions f and g of the corresponding Darboux transformations, can only be chosen from (adjoint) wave functions or (Lᵏ)<m=∑ᵢ₌₁ˡqᵢΔ⁻¹Λᵐrᵢ. Then successive applications of Darboux transformations for gcdKP hierarchy are discussed. Finally based upon above, solutions of gcdKP hierarchy are obtained from L^\0\=Λ by Darboux transformations.