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    Research Article|November 01 1992

    Constraints of the Kadomtsev–Petviashvili hierarchy

    Yi Cheng
    Yi Cheng
    Department of Mathematics, University of Science and Technology of China, Hefei 230026, Anhui, People’s Republic of China
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    Yi Cheng
    Department of Mathematics, University of Science and Technology of China, Hefei 230026, Anhui, People’s Republic of China
    J. Math. Phys. 33, 3774–3782 (1992)
    Article history
    Received:
    April 17 1992
    Accepted:
    June 29 1992
    Citation

    Yi Cheng; Constraints of the Kadomtsev–Petviashvili hierarchy.J. Math. Phys. 1 November 1992; 33 (11): 3774–3782.https://doi.org/10.1063/1.529875

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      For the Kadomtsev–Petviashvili (KP) hierarchy constructed in terms of the famous Sato theory, a ‘‘k constraint’’ is proposed that leads the hierarchy to the nonlinear system involving a finite number of dynamical coordinates. The eigenvalue problem of thek‐constrained system is naturally obtained from the linear system of the KP hierarchy, which takes the form ofkth‐order polynomial coupled with a first‐order one, thus we are able to derive the correspondent Lax pair, recursion operator, bi‐Hamiltonian structures, and conserved quantities. The constraints for the BKP hierarchy are also sketched.

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