Riemann-Hilbert problem for the focusing nonlinear Schrödinger equation with multiple high-order poles under nonzero boundary conditions
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Publication:2670237
DOI10.1016/J.PHYSD.2022.133162zbMATH Open1487.35272arXiv2104.00966OpenAlexW4226021046WikidataQ114141941 ScholiaQ114141941MaRDI QIDQ2670237
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Publication date: 10 March 2022
Published in: (Search for Journal in Brave)
Abstract: The Riemann-Hilbert (RH) problem is first developed to study the focusing nonlinear Schr"{o}dinger (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. Further, the solution of RH problem is transformed into a closed system of algebraic equations, and the soliton solutions corresponding to the transmission coefficient with an -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 is given as example.
Full work available at URL: https://arxiv.org/abs/2104.00966
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