Solutions of a generalized constrained discrete KP (gcdKP) hierarchy with constraint on Lax operator $L^k=(L^k)_{ \geq m}+\sum_{ i=1}^lq_i\Delta^{ -1}\Lambda^mr_i$, are invesitigated by Darboux transformations $T_D(f)=f^{ [1]}\cdot\Delta\cdot f^{ -1}$ and $T_I(g)=(g^{ [-1]})^{ -1}\cdot\Delta^{ -1}\cdot g$. 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 $(L^k)_{ <m}=\sum_{ i=1}^lq_i\Delta^{ -1}\Lambda^mr_i$. Then successive applications of Darboux transformations for gcdKP hierarchy are discussed. Finally based upon above, solutions of gcdKP hierarchy are obtained from $L^{ \{ 0\}}=\Lambda$ by Darboux transformations.
Categories: nlin.SI math-ph math.MP