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.
|Number of pages||20|
|Journal||Journal of Physics A: Mathematical and General|
|Publication status||Published - 19 Nov 1999|
Scopus Subject Areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)