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

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  • Zeng, Yunbo

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.

Suggested Citation

  • Zeng, Yunbo, 1999. "Bi-hamiltonian structure of JM hierarchy with self-consistent sources," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 262(3), pages 405-419.
    • Handle: RePEc:eee:phsmap:v:262:y:1999:i:3:p:405-419
    DOI: 10.1016/S0378-4371(98)00428-2
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    Cited by:

    1. Lin, Runliang & Zeng, Yunbo & Ma, Wen-Xiu, 2001. "Solving the KdV hierarchy with self-consistent sources by inverse scattering method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 291(1), pages 287-298.

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