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Initial Value Problem for the Pair Transition Coupled Nonlinear Schrödinger Equations via the Riemann–Hilbert Method

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Abstract

In this work, the matrix Riemann–Hilbert problem of the pair transition coupled nonlinear Schrödinger (ptcNLS) equations is presented in the complex \(\zeta \)-plane. According to the unique solution of the resulting Riemann–Hilbert problem, the formal soliton solution to the initial value problem of the ptcNLS equations is derived ultimately.

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Acknowledgements

The authors would like to thank the editor and the referees for their valuable comments and suggestions. This work was supported by the Postgraduate Research and Practice of Educational Reform for Graduate students in CUMT under Grant No. 2019YJSJG046, the Natural Science Foundation of Jiangsu Province under Grant No. BK20181351, the Six Talent Peaks Project in Jiangsu Province under Grant No. JY-059, the Qinglan Project of Jiangsu Province of China, the National Natural Science Foundation of China under Grant No. 11975306, the Fundamental Research Fund for the Central Universities under the Grant Nos. 2019ZDPY07 and 2019QNA35, and the General Financial Grant from the China Postdoctoral Science Foundation under Grant Nos. 2015M570498 and 2017T100413.

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Authors and Affiliations

  1. School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou, 221116, People’s Republic of China

    Wei-Qi Peng, Shou-Fu Tian & Tian-Tian Zhang

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  1. Wei-Qi Peng
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  2. Shou-Fu Tian
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  3. Tian-Tian Zhang
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Correspondence to Shou-Fu Tian or Tian-Tian Zhang.

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Communicated by Fabrizio Colombo.

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Peng, WQ., Tian, SF. & Zhang, TT. Initial Value Problem for the Pair Transition Coupled Nonlinear Schrödinger Equations via the Riemann–Hilbert Method. Complex Anal. Oper. Theory 14, 38 (2020). https://doi.org/10.1007/s11785-020-00997-1

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