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Volume 26, Issue 2
A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations

Yingnan Zhang, Xingbiao Hu, Yi He & Jianqing Sun

DOI: 10.4208/cicp.OA-2018-0157

Commun. Comput. Phys., 26 (2019), pp. 579-598.

Published online: 2019-04

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  • 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.

  • Keywords

Toda-type equation, N-periodic wave solution, Riemann's θ-function, Gauss-Newton method.

  • AMS Subject Headings

37K10, 39A10, 39A23, 65H10, 65Q10

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-26-579, author = {Yingnan Zhang, Xingbiao Hu, Yi He and Jianqing Sun}, title = {A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0157}, url = {http://global-sci.org/intro/article_detail/cicp/13103.html} }
TY - JOUR T1 - A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations AU - Yingnan Zhang, Xingbiao Hu, Yi He & Jianqing Sun JO - Communications in Computational Physics VL - 2 SP - 579 EP - 598 PY - 2019 DA - 2019/04 SN - 26 DO - http://doi.org/10.4208/cicp.OA-2018-0157 UR - https://global-sci.org/intro/article_detail/cicp/13103.html KW - Toda-type equation, N-periodic wave solution, Riemann's θ-function, Gauss-Newton method. AB -

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.

Yingnan Zhang, Xingbiao Hu, Yi He and Jianqing Sun. (2019). A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations. Communications in Computational Physics. 26 (2). 579-598. doi:10.4208/cicp.OA-2018-0157
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