2024/07/31 by Meisen Chen, Chen, Meisen, Engui Fan +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2407.21526
openalex publication_date 2024/07/31 · openalex created_date 2024/08/04 · openalex updated_date 2026/07/28
We investigate the soliton resolution and Painlevé asymptotics for the focusing Ablowitz-Ladik system with the initial data in a discrete weighted ℓ2 space. First, we establish the global well-posedness of this initial-value problem, which is further reformulated as a Riemann-Hilbert problem with higher-order poles. Using Fredholm theory, the Riemann-Hilbert problem with the jump contour consisting of three circles centered around the origin is uniquely solved. Then, by performing a ∂-nonlinear steepest descent method to the Riemann-Hilbert problem, we obtain the asymptotic approximation to the solution of the focusing Ablowitz-Ladik system for large time in different space-time regions of the (n,t)-half plane. In the sectors \(n,t): n /(2t) <-M0 \ and \(n,t): n /(2t) >M0 \, where M0 is a positive constant, the leading order asymptotics is dominated by the solitons; while in the sector \(n,t): |n /(2t) -1