Regular solution and lattice Miura transformation of bigraded Toda hierarchy
Regular solution and lattice Miura transformation of bigraded Toda hierarchy
复制标题
DOI：
10.1007/s11401-013-0804-x
复制
发表时间：
2012-10
期刊：
影响因子：
--
通讯作者：
Chuanzhong Li;Jingsong He
中科院分区：
文献类型：
--
作者：
Chuanzhong Li;Jingsong He
作者给出了双级 Toda 层次结构 (BTH) 的有限维指数解。作为 BTH 指数解的具体示例，作者考虑了具有 3 × 3 大小的 Lax 矩阵的 (1, 2)-BTH 的正则解，并讨论了该解的一些几何结构，从中显示了 (1, 2)-BTH 与原始 Toda 层次结构之间的差异。此后，作者构造了(N,1)-BTH的另一种Lax表示，该表示不使用Lax算子的分数算子。然后作者介绍了(N,1)-BTH的晶格Miura变换，该变换导出了取决于一个场的方程，同时给出了一些包含Volterra晶格方程（一种有用的生态竞争模型）的具体例子。
The authors give finite dimensional exponential solutions of the bigraded Toda hierarchy (BTH). As a specific example of exponential solutions of the BTH, the authors consider a regular solution for the (1, 2)-BTH with a 3 × 3-sized Lax matrix, and discuss some geometric structures of the solution from which the difference between the (1, 2)-BTH and the original Toda hierarchy is shown. After this, the authors construct another kind of Lax representation of (N, 1)-BTH which does not use the fractional operator of Lax operator. Then the authors introduce the lattice Miura transformation of (N, 1)-BTH which leads to equations depending on one field, and meanwhile some specific examples which contain the Volterra lattice equation (a useful ecological competition model) are given.