TY - JOUR T1 - A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations 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.