## Abstract

The nonlinearization of the eigenvalue problems associated with the Toda hierarchy and the coupled Korteweg - de Vries (KdV) hierarchy leads to an integrable symplectic map S and an integrable Hamiltonian system (H_{0}), respectively. It is proved that S and (H_{0}) have the same integrals [H_{k}]. The quasi-periodic solution of the (2 + 1)-dimensional Kadomtsev - Petviashvili equation is split into three Hamiltonian systems (H_{0}), (H_{1}), (H_{2}), while that of the special (2 + 1)-dimensional Toda equation is separated into (H_{0}), (H_{1}) plus the discrete flow generated by the symplectic map S. A clear evolution picture of various flows is given through the 'window' of Abel - Jacobi coordinates. The explicit theta-function solutions are obtained by resorting to this separation technique.

Original language | English |
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Pages (from-to) | 8059-8078 |

Number of pages | 20 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 32 |

Issue number | 46 |

DOIs | |

Publication status | Published - 19 Nov 1999 |

Externally published | Yes |

## Scopus Subject Areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)