TY - JOUR
T1 - From the special 2 + 1 Toda lattice to the Kadomtsev - Petviashvili equation
AU - Cao, Cewen
AU - Geng, Xianguo
AU - Wu, Yongtang
PY - 1999/11/19
Y1 - 1999/11/19
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0033584758&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/32/46/306
DO - 10.1088/0305-4470/32/46/306
M3 - Journal article
AN - SCOPUS:0033584758
SN - 0305-4470
VL - 32
SP - 8059
EP - 8078
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 46
ER -