From the special 2 + 1 Toda lattice to the Kadomtsev - Petviashvili equation

Cewen Cao*, Xianguo Geng, Yongtang Wu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

105 Citations (Scopus)


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 (H0), respectively. It is proved that S and (H0) have the same integrals [Hk]. The quasi-periodic solution of the (2 + 1)-dimensional Kadomtsev - Petviashvili equation is split into three Hamiltonian systems (H0), (H1), (H2), while that of the special (2 + 1)-dimensional Toda equation is separated into (H0), (H1) 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 languageEnglish
Pages (from-to)8059-8078
Number of pages20
JournalJournal of Physics A: Mathematical and General
Issue number46
Publication statusPublished - 19 Nov 1999
Externally publishedYes

Scopus Subject Areas

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


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