Bi-hamiltonian structure of JM hierarchy with self-consistent sources

By taking the space variable x as the evolution parameter and introducing t he Jacobi-Ostrogradiski coordinates, we present t-type hamiltonian descript ion of soliton equations with self-consistent sources which have not x-type hamiltonian formulation when considering t as evolution parameter. The t-t ype Miura map generates the second hamiltonian structure for these t-type h amiltonian systems. The two compatible hamiltonian operators are used to co nstruct a hereditary operator and to obtain new hierarchies of infinite-dim ensional integrable Hamiltonian systems. The reduction of these equations w ith sources gives rise to the constrained flows of soliton equations and th eir bi-hamiltonian structure. We use the Jaulent-Miodek hierarchy with self -consistent sources to illustrate the method. (C) 1999 Elsevier Science B.V . All rights reserved.