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.

中文翻译：

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离散离焦mKdV方程的长时间渐近行为

在本文中，我们应用Deift-Zhou非线性最速下降方法来分析离散离焦mKdV方程$$ \ begin {aligned} \ dot {q} _n = \ left（1-q_n ^ 2 \ right）\ left（q_ {n + 1} -q_ {n-1} \ right）\ end {aligned} $$具有衰减初始值$$ \ begin {aligned} q_n（t = 0）= q_n （0），\ end {aligned} $$，其中\（n = 0，\ pm 1，\ pm 2，\ ldots \）是离散变量，t是连续时间变量。该方程式由Ablowitz和Ladik提出。