A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations (Communications in Computational Physics, 2019)
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 andthen use the Gauss-Newton method to solve it. By use of this numerical scheme, wecalculate the 3-periodic wave solutions to some discrete integrable equations such asthe Toda lattice equation, the Lotka-Volterra equation, the differential-difference KPequation and so on.
Keywords: Toda-type equation; N-periodic wave solution; Riemann's θ-function; Gauss-Newton method.