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The general fifth-order nonlinear Schrödinger equation with nonzero boundary conditions: Inverse scattering transform and multisoliton solutions

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Abstract

We study the inverse scattering transform of the general fifth-order nonlinear Schrödinger (NLS) equation with nonzero boundary conditions (NZBCs), which can be reduced to several integrable equations. First, a matrix Riemann–Hilbert problem (RHP) for the fifth-order NLS equation with NZBCs at infinity is systematically investigated. Moreover, the inverse problems are solved by studying a matrix RHP. We construct the general solutions for reflectionless potentials. The trace formulas and theta conditions are also presented. In particular, we analyze the simple-pole and double-pole solutions for the fifth-order NLS equation with NZBCs. Finally, we discuss the dynamics of the obtained solutions in terms of their plots. The results in this work should be helpful in explaining and enriching the nonlinear wave phenomena in nonlinear fields.

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Funding

This work is supported by the National Natural Science Foundation of China under Grant No. 11871180.

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  1. Department of Mathematics, Harbin Institute of Technology, Harbin, China

    Xiu-Bin Wang & Bo Han

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  1. Xiu-Bin Wang
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  2. Bo Han
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Correspondence to Xiu-Bin Wang.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2022, Vol. 210, pp. 11–37 https://doi.org/10.4213/tmf10149.

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Wang, XB., Han, B. The general fifth-order nonlinear Schrödinger equation with nonzero boundary conditions: Inverse scattering transform and multisoliton solutions. Theor Math Phys 210, 8–30 (2022). https://doi.org/10.1134/S0040577922010020

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