Discrete Two-Dimensional Toda Molecule Equation
Discrete Two-Dimensional Toda Molecule Equation
复制标题
离散二维 Toda 分子方程
DOI：
10.1143/jpsj.56.4285
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发表时间：
1987
影响因子：
1.7
通讯作者：
R. Hirota
中科院分区：
文献类型：
--
作者：
R. Hirota
得到了二维Toda分子方程的离散模拟，表示为 \begin{aligned} \varDelta＿x{}\varDelta ＿yQ＿n{(x,y)}={V＿n+1}(x,y)-{V＿n}(x+ {}{}\delta,y)-{V＿n}(x,y+ \varepsilon)+{V＿n-1}(x+ \delta,y+ \varepsilon)， \end{aligned} 在哪里 \begin{aligned} V＿n{(x,y)}={(}\delta\varepsilon)^{-1}\log[1+\delta\varepsilon\exp[Q_{n}(x,y)]]， \end{aligned} 边界条件为v0 (x, y)= vn +1 (x, y)=0。符号Δ z表示相对于z的正向差分算子，Δ和e是与区间有关的参数。它的精确解用卡索拉蒂行列式表示。
A discrete analogue of the two-dimensional Toda molecule equation is obtained, which is expressed as follows \begin{aligned} \varDelta_{x}\varDelta_{y}Q_{n}(x,y){=}V_{n+1}(x,y)-V_{n}(x+\delta,y)-V_{n}(x,y+\varepsilon)+V_{n-1}(x+\delta,y+\varepsilon), \end{aligned} where \begin{aligned} V_{n}(x,y){=}(\delta\varepsilon)^{-1}\log[1+\delta\varepsilon\exp[Q_{n}(x,y)]], \end{aligned} with the boundary conditions V 0 ( x , y )= V n +1 ( x , y )=0. The symbol Δ z denotes the forward difference operator with respect to z , and δ and e are parameters relating to infervals. Exact solutions to it are expressed with Casorati determinants.