Journal of Nonlinear Mathematical Physics

Volume 28, Issue 1, March 2021, Pages 134 - 149

The Complex Hamiltonian Systems and Quasi-periodic Solutions in the Hirota Equation

Authors
Jinbing Chen*, Rong Tong
School of Mathematics, Southeast University, Nanjing, Jiangsu 210096, P. R. China
*Corresponding author. Email: cjb@seu.edu.cn
Corresponding Author
Jinbing Chen
Received 7 May 2020, Accepted 21 August 2020, Available Online 10 December 2020.
DOI
https://doi.org/10.2991/jnmp.k.200922.010How to use a DOI?
Keywords
Hirota equation, complex finite-dimensional Hamiltonian system, quasi-periodic solution
Abstract

The Hirota equation is reduced to a pair of complex Finite-dimensional Hamiltonian Systems (FDHSs) with real-valued Hamiltonians, which are proven to be completely integrable in the Liouville sense. It turns out that involutive solutions of the complex FDHSs yield finite parametric solutions of the Hirota equation. From a Lax matrix of the complex FDHSs, the Hirota flow is linearized to display its evolution behavior on the Jacobi variety of a Riemann surface. With the technique of Riemann–Jacobi inversion, the quasi-periodic solution of the Hirota equation is presented in the form of Riemann theta functions.

Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)
View full text (HTML)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
28 - 1
Pages
134 - 149
Publication Date
2020/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.k.200922.010How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Jinbing Chen
AU  - Rong Tong
PY  - 2020
DA  - 2020/12
TI  - The Complex Hamiltonian Systems and Quasi-periodic Solutions in the Hirota Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 134
EP  - 149
VL  - 28
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.k.200922.010
DO  - https://doi.org/10.2991/jnmp.k.200922.010
ID  - Chen2020
ER  -