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Riemann–Hilbert problem for the Kundu-type nonlinear Schrödinger equation with \(N\) distinct arbitrary-order poles

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Abstract

We use the Riemann–Hilbert (RH) method to study the Kundu-type nonlinear Schrödinger (Kundu–NLS) equation with a zero boundary condition in the case where the scattering coefficient has \(N\) distinct arbitrary-order poles. We perform a spectral analysis of the Lax pair and consider the asymptotic property, symmetry, and analyticity of the Jost solution. Based on these results, we formulate the RH problem whose solution allows solving the considered Kundu–NLS equation. In addition, using graphic analysis, we study the characteristics of soliton solutions of some particular cases of the problem with \(N\) distinct arbitrary-order poles.

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Acknowledgments

The authors sincerely thank the editor and referees for their valuable comments.

Funding

This research was supported by the National Natural Science Foundation of China (Grant No. 11975306), the Natural Science Foundation of Jiangsu Province (Grant No. BK20181351), the Six Talent Peaks Project in Jiangsu Province (Grant No. JY-059), and the Fundamental Research Fund for the Central Universities (Grant Nos. 2019ZDPY07 and 2019QNA35).

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  1. School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou, China

    Zi-Yi Wang, Shou-Fu Tian & Xiao-Fan Zhang

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  1. Zi-Yi Wang
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  2. Shou-Fu Tian
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Correspondence to Shou-Fu Tian.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 207, pp. 23-43 https://doi.org/10.4213/tmf10015.

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Wang, ZY., Tian, SF. & Zhang, XF. Riemann–Hilbert problem for the Kundu-type nonlinear Schrödinger equation with \(N\) distinct arbitrary-order poles. Theor Math Phys 207, 415–433 (2021). https://doi.org/10.1134/S0040577921040024

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