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
- 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/).
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TY - JOUR AU - Jinbing Chen AU - Rong Tong PY - 2020 DA - 2020/12/10 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 - 10.2991/jnmp.k.200922.010 ID - Chen2020 ER -