期刊
PHYSICA D-NONLINEAR PHENOMENA
卷 432, 期 -, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.physd.2022.133162
关键词
The focusing nonlinear Schrodinger equation; Riemann-Hilbert problem; Multiple high-order poles; Nonzero boundary conditions
资金
- National Natu-ral Science Foundation of China [11975306]
- Natural Science Foundation of Jiangsu Province [BK20181351]
- Six Talent Peaks Project in Jiangsu Province [JY-059]
- Fundamental Research Fund for the Central Universities [2019ZDPY07, 2019QNA35]
The Riemann-Hilbert problem is developed to study the focusing behavior of the nonlinear Schrodinger equation with multiple high-order poles. By employing Laurent expansion and solving an algebraic system, soliton solutions corresponding to the transmission coefficient are obtained.
The Riemann-Hilbert (RH) problem is developed to study the focusing nonlinear Schrodinger (NLS) equation with multiple high-order poles under nonzero boundary conditions. Laurent expansion and Taylor series are employed to replace the residues at the simple-and the second-poles. Furthermore, the solution of RH problem is transformed into a closed system of algebraic equations, and the soliton solutions corresponding to the transmission coefficient 1/s(11)(z) with an N-order pole are obtained by solving the algebraic system. Then, in a more general case, the transmission coefficient with multiple high-order poles is studied, and the corresponding solutions are obtained. In addition, for high-order pole, the propagation behavior of the soliton solution corresponding to a third-order pole and the mixed case of a second-order pole and a simple pole are given as example. (C) 2022 Elsevier B.V. All rights reserved.
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