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Long-time asymptotics for the initial-boundary value problem of coupled Hirota equation on the half-line

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Abstract

The object of this work is to investigate the initial-boundary value problem for coupled Hirota equation on the half-line. We show that the solution of the coupled Hirota equation can be expressed in terms of the solution of a 3 × 3 matrix Riemann-Hilbert problem formulated in the complex k-plane. The relevant jump matrices are explicitly given in terms of the matrix-valued spectral functions s(k) and S(k) that depend on the initial data and boundary values, respectively. Then, applying nonlinear steepest descent techniques to the associated 3 × 3 matrix-valued Riemann-Hilbert problem, we can give the precise leading-order asymptotic formulas and uniform error estimates for the solution of the coupled Hirota equation.

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Acknowledgements

This work was supported by the China Postdoctoral Science Foundation (Grant No. 2019TQ0041).

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Nan Liu & Boling Guo

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  1. Nan Liu
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  2. Boling Guo
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Correspondence to Nan Liu.

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Liu, N., Guo, B. Long-time asymptotics for the initial-boundary value problem of coupled Hirota equation on the half-line. Sci. China Math. 64, 81–110 (2021). https://doi.org/10.1007/s11425-018-9567-1

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