The regularity of the multiple higher-order poles solitons of the NLS equation
The regularity of the multiple higher-order poles solitons of the NLS equation
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NLS方程的多个高阶极孤子的正则性
DOI：
10.1111/sapm.12338
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发表时间：
2020
影响因子：
2.7
通讯作者：
He Jing-Song
中科院分区：
文献类型：
--
作者：
Zhang Yong-Shuai;Tao Xiang-Xing;Yao Teng-Teng;He Jing-Song
基于逆散射方法，得到了非线性薛定谔方程（NLS）的单高阶极点孤子和多高阶极点孤子的计算公式.它们的共轭因子表示为，其中是一个经常用于求解黎曼-希尔伯特问题的矩阵，星号表示复共轭。我们采用两种方法证明了它是可逆的。第一个证明矩阵等价于自伴汉克尔矩阵，证明。第二个考虑块矩阵形式，证明。另外，我们证明了的维数等价于传递系数的极点阶数之和，它的对角元构成一组基。
Based on the inverse scattering method, the formulae of one higher‐order pole solitons and multiple higher‐order poles solitons of the nonlinear Schrödinger equation (NLS) equation are obtained. Their denominators are expressed as , where is a matrix frequently constructed for solving the Riemann‐Hilbert problem, and the asterisk denotes complex conjugate. We take two methods for proving is invertible. The first one shows matrix is equivalent to a self‐adjoint Hankel matrix , proving . The second one considers the block‐matrix form of , proving . In addition, we prove that the dimension of is equivalent to the sum of the orders of pole points of the transmission coefficient and its diagonal entries compose a set of basis.