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Pure soliton solutions of the nonlocal Kundu–nonlinear Schrödinger equation

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Abstract

We systematically present an inverse scattering transform for a nonlocal reverse-space higher-order nonlinear Schrödinger equation with nonzero boundary conditions at infinity. We discuss two cases determined by two different values of the phase at infinity. In particular, for the direct problem, we study the analytic properties of the scattering data and the eigenfunctions and also find their symmetries. We study the inverse scattering problem obtained from the new nonlocal system using left and right Riemann–Hilbert problems with a suitable uniformization variable; we construct the time dependence of the scattering data. Finally, for these two phase values, we analyze the dynamics of solitons (solutions of the considered Schrödinger equation) in detail.

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Funding

This research is supported by the National Natural Science Foundation of China (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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Wang, XB., Han, B. Pure soliton solutions of the nonlocal Kundu–nonlinear Schrödinger equation. Theor Math Phys 206, 40–67 (2021). https://doi.org/10.1134/S0040577921010037

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