Exact solutions for two dimensional Dn(1) Toda equation
Exact solutions for two dimensional Dn(1) Toda equation
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DOI：
10.1016/j.cnsns.2023.107792
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发表时间：
2023-12
期刊：
影响因子：
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通讯作者：
Yu-Yue Li;Zi-Xiang Zhou
中科院分区：
文献类型：
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作者：
Yu-Yue Li;Zi-Xiang Zhou
对于对应于Kac Moody代数Dn（1）的二维户田方程，构造了Darboux变换.这个方程的Lax对的系数矩阵是偶数阶的。与二维A2 n（2），Cn（1）和Dn + 1（2）户田方程的达布矩阵中的标量相比，该方程的达布矩阵中的2× 2块的结构要复杂得多.在达布矩阵的构造中，要求Lax对的解在Lag（n = 2n）中.借助于Lag（n，n）的稠密子集，达布矩阵的非平凡块用O（n，n）的元素表示.本文利用代数技巧对达布矩阵进行了简化，证明了达布矩阵的形式只与n的奇偶性有关。
For the two dimensional Toda equation corresponding to the Kac–Moody algebra D n (1), the Darboux transformation is constructed. The coefficient matrices of the Lax pair of this equation are of even order. Comparing with the scalars in the Darboux matrices for the two dimensional A 2 n (2), C n (1) and D n+ 1 (2) Toda equations, the structure of the 2× 2 blocks in the Darboux matrix for this equation is much more complicated. In the construction of Darboux matrices, it is demanded that the solutions of the Lax pair are in Lag (ℂ 2 n). With the help of a dense subset of Lag (ℂ 2 n), the nontrivial blocks of the Darboux matrices are represented by elements of O (n, ℂ). Quite a few algebraic techniques are used to simplify the Darboux matrices and to show that the form of the Darboux matrices only depends on the parity of n.