Degenerate Solutions of the Nonlinear Self-Dual Network Equation
Degenerate Solutions of the Nonlinear Self-Dual Network Equation
复制标题
DOI：
10.1088/0253-6102/71/1/1
复制
发表时间：
2019
影响因子：
3.1
通讯作者：
贺劲松 李茂华 邱迎阳;Jing-Song He Mao-Hua Li Ying-Yang Qiu
中科院分区：
文献类型：
--
作者：
贺劲松 李茂华 邱迎阳;Jing-Song He Mao-Hua Li Ying-Yang Qiu
The N-fold Darboux transformation (DT) T [N] n of the nonlinear self-dual network equation is given in terms of the determinant representation. The elements in determinants are composed of the eigenvalues λj (j= 1, 2..., N) and the corresponding eigenfunctions of the associated Lax equation. Using this representation, the N-soliton solutions of the nonlinear self-dual network equation are given from the zero “seed” solution by the N-fold DT. A general form of the N-degenerate soliton is constructed from the determinants of N-soliton by a special limit λj→ λ1 and by using the higher-order Taylor expansion. For 2-degenerate and 3-degenerate solitons, approximate orbits are given analytically, which provide excellent fit of exact trajectories. These orbits have a time-dependent “phase shift”, namely ln (t2).
