The Lotka-Volterra Equations and the QR Algorithm
The Lotka-Volterra Equations and the QR Algorithm
复制标题
Lotka-Volterra 方程和 QR 算法
DOI：
10.1143/jpsj.64.3669
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发表时间：
1995
影响因子：
1.7
通讯作者：
J. Satsuma
中科院分区：
文献类型：
--
作者：
A. Nagai;J. Satsuma
结果表明，利用QR算法生成了求解给定矩阵特征值的Lotka-Volterra方程组的层次结构。层次结构中的一个方程是d N k / d t = N k {N k +1 (N k + N k +1 + N k +2) - N k -1 (N k -2 + N k -1 + N k)}，其中一个物种与其他四个物种相互作用。讨论了该层次结构与Toda格层次结构的关系。此外，利用双线性形式研究了孤子解的结构。
It is shown that a hierarchy of the Lotka-Volterra equations is generated from the QR algorithm to find eigenvalues of a given matrix. One of the equations in the hierarchy is given by d N k / d t = N k { N k +1 ( N k + N k +1 + N k +2 ) - N k -1 ( N k -2 + N k -1 + N k )}, in which one species interacts with other four species. The relation between this hierarchy and the Toda lattice hierarchy is discussed. Moreover, the structure of soliton solutions is studied by means of the bilinear formalism.