Abstract
By taking the space variable x as the evolution parameter and introducing the Jacobi–Ostrogradiski coordinates, we present t-type hamiltonian description of soliton equations with self-consistent sources which have not x-type hamiltonian formulation when considering t as evolution parameter. The t-type Miura map generates the second hamiltonian structure for these t-type hamiltonian systems. The two compatible hamiltonian operators are used to construct a hereditary operator and to obtain new hierarchies of infinite-dimensional integrable Hamiltonian systems. The reduction of these equations with sources gives rise to the constrained flows of soliton equations and their bi-hamiltonian structure. We use the Jaulent–Miodek hierarchy with self-consistent sources to illustrate the method.
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