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The Riemann–Hilbert approach for the Chen–Lee–Liu equation and collisions of multiple solitons

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Abstract

We consider the Riemann–Hilbert method for the Chen–Lee–Liu equation with a vanishing boundary condition. By analyzing the asymptotic, analytic, and symmetric properties of the Jost solutions, we display the expression of scattering coefficients, theta condition, and the residue conditions. A revised Riemann–Hilbert problem (RHP) is constructed from the Jost solutions, which satisfies the normalization condition. By assuming that the RHP has simple poles, we solve the RHP and display the raw formulae for N-th order solitons of the CLL equation. By applying the Cauchy–Binent formula, we present the explicit formulae for N-th order solitons and consider the exciting collisions of the multiple solitons.

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Funding

This work is supported by the National Natural Science Foundation of China (Grant Nos. 12171433).

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Authors and Affiliations

  1. Department of Mathematics, Shaoxing University, Shaoxing, 312000, Zhejiang Province, People’s Republic of China

    Yongshuai Zhang

  2. Department of Mathematics, Lishui University, Lishui, 323000, Zhejiang Province, People’s Republic of China

    Bingwen Lin

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  1. Yongshuai Zhang
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Zhang, Y., Lin, B. The Riemann–Hilbert approach for the Chen–Lee–Liu equation and collisions of multiple solitons. Nonlinear Dyn 112, 3737–3748 (2024). https://doi.org/10.1007/s11071-023-09196-x

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