Year: 2019
Author: Yingnan Zhang, Xingbiao Hu, Yi He, Jianqing Sun
Communications in Computational Physics, Vol. 26 (2019), Iss. 2 : pp. 579–598
Abstract
In this paper, we present an efficient numerical scheme to calculate N-periodic wave solutions to the Toda-type equations. The starting point is the algebraic condition for having N-periodic wave solutions proposed by Akira Nakamura. The basic idea is to formulate the condition as a nonlinear least square problem and then use the Gauss-Newton method to solve it. By use of this numerical scheme, we calculate the 3-periodic wave solutions to some discrete integrable equations such as the Toda lattice equation, the Lotka-Volterra equation, the differential-difference KP equation and so on.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0157
Communications in Computational Physics, Vol. 26 (2019), Iss. 2 : pp. 579–598
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Toda-type equation N-periodic wave solution Riemann's θ-function Gauss-Newton method.
Author Details
-
Numerical evaluations of periodic wave solutions, integrable time discretization and their applications to the mKdV–sine-Gordon equation
Hu, Xingbiao | Pan, Yan | Sun, Jianqing | Wang, Hui | Zhang, YingnanJournal of Physics A: Mathematical and Theoretical, Vol. 53 (2020), Iss. 39 P.394001
https://doi.org/10.1088/1751-8121/aba85e [Citations: 6] -
Numerical calculation ofN-periodic wave solutions to coupled KdV–Toda-type equations
Zhang, Yingnan | Hu, Xingbiao | Sun, JianqingProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 477 (2021), Iss. 2245
https://doi.org/10.1098/rspa.2020.0752 [Citations: 6] -
Quasi-periodic breathers and their dynamics to the Fokas system in nonlinear optics
Xin, Pengcheng | Zhao, Zhonglong | Wang, YuWave Motion, Vol. 133 (2025), Iss. P.103449
https://doi.org/10.1016/j.wavemoti.2024.103449 [Citations: 0] -
Numerical calculation of N-periodic wave solutions to two kinds of generalized (2+1)-dimensional KdV-type equations
Xin, Pengcheng | Zhao, Zhonglong | Wang, Yu | Guo, Zun-GuangPhysica Scripta, Vol. 100 (2025), Iss. 1 P.015257
https://doi.org/10.1088/1402-4896/ad9ae3 [Citations: 0] -
The N-periodic wave solutions to the N = 1 supersymmetric Sawada–Kotera–Ramani equation
Xin 辛, Pengcheng 鹏程 | Zhao 赵, Zhonglong 忠龙 | Wang 王, Yu 宇Chinese Physics B, Vol. 34 (2025), Iss. 2 P.020502
https://doi.org/10.1088/1674-1056/ad9912 [Citations: 0] -
Integrable Variants of the Toda Lattice
Liu, Ya-Jie | Wang, Hui Alan | Chang, Xiang-Ke | Hu, Xing-Biao | Zhang, Ying-NanJournal of Nonlinear Science, Vol. 34 (2024), Iss. 5
https://doi.org/10.1007/s00332-024-10072-0 [Citations: 0] -
Canonical solution and singularity propagations of the nonlocal semi-discrete Schrödinger equation
Chen, Kui | Na, Chongning | Yang, JiaxiNonlinear Dynamics, Vol. 111 (2023), Iss. 2 P.1685
https://doi.org/10.1007/s11071-022-07912-7 [Citations: 2] -
A numerical study of N-periodic wave solutions to four integrable equations
Liang, Zhuo-Yao | Sun, Jian-Qing | Yu, Guo-Fu | Zhong, Yi-NingCommunications in Nonlinear Science and Numerical Simulation, Vol. 116 (2023), Iss. P.106858
https://doi.org/10.1016/j.cnsns.2022.106858 [Citations: 3] -
A numerical study on the N-periodic wave solutions of two coupled bilinear equations
Wang, Xue-Xia | Sun, Jian-Qing | Zhang, Ying-NanNumerical Algorithms, Vol. 88 (2021), Iss. 2 P.711
https://doi.org/10.1007/s11075-020-01054-w [Citations: 8]