The regularity of the multiple higher-order poles solitons of the NLS equation |
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Authors: | Yongshuai Zhang Xiangxing Tao Tengteng Yao Jingsong He |
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Affiliation: | 1. School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, China;2. Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong, China |
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Abstract: | 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. |
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Keywords: | higher-order poles initial value problem nonlinear Schrödinger equation regularity Riemann-Hilbert problem |
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