Yu Zhang, Zhang Yufeng
College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, 266510, PR China.
Chaos Solitons Fractals. 2009 Jan 15;39(1):399-406. doi: 10.1016/j.chaos.2007.04.011.
With the help of invertible linear transformations and the known Lie algebras, a higher-dimensional 6 x 6 matrix Lie algebra smu(6) is constructed. It follows a type of new loop algebra is presented. By using a (2 + 1)-dimensional partial-differential equation hierarchy we obtain the integrable coupling of the (2 + 1)-dimensional KN integrable hierarchy, then its corresponding Hamiltonian structure is worked out by employing the quadratic-form identity. Furthermore, a higher-dimensional Lie algebra denoted by E, is given by decomposing the Lie algebra smu(6), then a discrete lattice integrable coupling system is produced. A remarkable feature of the Lie algebras smu(6) and E is used to directly construct integrable couplings.
借助可逆线性变换和已知李代数，构造了一个高维6×6矩阵李代数smu(6)。由此给出了一种新型的环代数。利用一个(2 + 1)维偏微分方程族得到了(2 + 1)维KN可积族的可积耦合，然后通过二次型恒等式求出了其相应的哈密顿结构。此外，通过对李代数smu(6)进行分解得到了一个由E表示的高维李代数，进而产生了一个离散格点可积耦合系统。利用李代数smu(6)和E的一个显著特征直接构造可积耦合。
