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Long-Time Asymptotic Behavior for the Discrete Defocusing mKdV Equation

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Abstract

In this article, we apply Deift–Zhou nonlinear steepest descent method to analyze the long-time asymptotic behavior of the solution for the discrete defocusing mKdV equation

$$\begin{aligned} \dot{q}_n = \left( 1-q_n^2\right) \left( q_{n+1}-q_{n-1}\right) \end{aligned}$$

with decay initial value

$$\begin{aligned} q_n(t=0) = q_n(0), \end{aligned}$$

where \(n=0,\pm 1,\pm 2,\ldots \) is a discrete variable and t is continuous time variable. This equation was proposed by Ablowitz and Ladik.

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Acknowledgements

Many thanks for referees for helpful suggestions in improving the manuscript. This work was supported by the National Science Foundation of China under Project Nos. 11671095 and 51879045.

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Authors and Affiliations

  1. School of Mathematical Science, Fudan University, Shanghai, 200433, People’s Republic of China

    Meisen Chen & Engui Fan

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  1. Meisen Chen
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  2. Engui Fan
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Correspondence to Engui Fan.

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Communicated by Dr. Anthony Bloch.

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Chen, M., Fan, E. Long-Time Asymptotic Behavior for the Discrete Defocusing mKdV Equation. J Nonlinear Sci 30, 953–990 (2020). https://doi.org/10.1007/s00332-019-09596-7

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