A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations
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.
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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
Yingnan Zhang Email
Xingbiao Hu Email
Yi He Email
Jianqing Sun Email
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