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 - <p style="text-align: justify;">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.</p>