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

Cewen Cao; Xianguo Geng; Yongtang Wu

doi:10.1088/0305-4470/32/46/306

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 journal › Article › peer-review

103 Citations (Scopus)

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 (H₀), respectively. It is proved that S and (H₀) have the same integrals [H_k]. 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 language	English
Pages (from-to)	8059-8078
Number of pages	20
Journal	Journal of Physics A: Mathematical and General
Volume	32
Issue number	46
DOIs	https://doi.org/10.1088/0305-4470/32/46/306
Publication status	Published - 19 Nov 1999
Externally published	Yes

Scopus Subject Areas

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

Access to Document

10.1088/0305-4470/32/46/306

Cite this

@article{a002eb3666f0413eb21f879543806981,

title = "From the special 2 + 1 Toda lattice to the Kadomtsev - Petviashvili equation",

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 (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.",

author = "Cewen Cao and Xianguo Geng and Yongtang Wu",

year = "1999",

month = nov,

day = "19",

doi = "10.1088/0305-4470/32/46/306",

language = "English",

volume = "32",

pages = "8059--8078",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing Ltd.",

number = "46",

}

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 - Article

AN - SCOPUS:0033584758

SN - 1751-8113

VL - 32

SP - 8059

EP - 8078

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 46

ER -

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

Abstract

Scopus Subject Areas

Access to Document

Other files and links

Fingerprint

Cite this