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arXiv · 2207.07387

Long-time asymptotic analysis for defocusing Ablowitz-Ladik system with initial value in lower regularity

Chen Meisen·Fan Engui·He Jingsong
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Abstract

Recently, we have given the $l^2$ bijectivity for defocusing Ablowitz-Ladik systems in the discrete Sobolev space $l^{2,1}$ by inverse spectral method. Based on these results, the goal of this article is to investigate the long-time asymptotic property for the initial-valued problem of the defocusing Ablowitz-Ladik system with initial potential in lower regularity. The main idea is to perform proper deformations and analysis to the corespondent Riemann-Hilbert problem with the unit circle as the jump contour $\Sigma$. As a result, we show that when $|\frac{n}{2t}|\le 1<1$, the solution admits Zakharov-Manakov type formula, and when $|\frac{n}{2t}|\ge 1>1$, the solution decays fast to zero.

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Chen Meisen, Fan Engui, He Jingsong. 2022-07-15. Long-time asymptotic analysis for defocusing Ablowitz-Ladik system with initial value in lower regularity. https://arxiv.org/abs/2207.07387

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