Long-time asymptotics for the defocusing Ablowitz-Ladik system with initial data in lower regularity

Recently, we have established the l(2) bijectivity for the defocusing Ablowitz-Ladik system in the discrete weighted space l(2 ,k) with k is an element of N+ by the inverse spectral method. Based on these results, our study is to investigate the long-time asymptotics for the initial -value problem of the defocusing Ablowitz-Ladik system with initial potential in lower regularity without rapid decay. In this case, since the reflection coefficient is not smooth enough, it is impossible to directly apply the nonlinear steepest descent method. Our main idea is to transform the corresponding Riemann-Hilbert problem on the unit circle as the jump contour into a partial derivative<overline>- Riemann-Hilbert problem to be handled. As a result, we show that the solution admits the Zakharov-Manakov type formula in the region |n/2t | <= V-0 < 1, while the solution decays fast to zero in the region |n/2t | >= V-0 < 1. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. partial derivative <overline>-