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Spectral Analysis and Long-time Asymptotics for the Coherently-coupled Nonlinear Schrödinger System

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Abstract

On the basis of the spectral analysis of the 4×4 matrix Lax pair, the initial value problem of the coherently-coupled nonlinear Schrödinger system is transformed into a 4×4 matrix Riemann-Hilbert problem. By using the nonlinear steepest decent method, the long-time asymptotics of the solution of the initial value problem for the coherently-coupled nonlinear Schrödinger system is obtained through deforming the Riemann-Hilbert problem into a solvable model one.

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Acknowledgments

We thank the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, P. R. China

    Ming Ming Chen, Xian Guo Geng & Ke Dong Wang

Authors
  1. Ming Ming Chen
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  2. Xian Guo Geng
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  3. Ke Dong Wang
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Corresponding author

Correspondence to Xian Guo Geng.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 11871440 and 11931017)

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Chen, M.M., Geng, X.G. & Wang, K.D. Spectral Analysis and Long-time Asymptotics for the Coherently-coupled Nonlinear Schrödinger System. Acta. Math. Sin.-English Ser. 38, 2090–2114 (2022). https://doi.org/10.1007/s10114-022-1109-3

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  • DOI: https://doi.org/10.1007/s10114-022-1109-3

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