THE MODIFIED KORTEWEG-DE VRIES LIMIT OF THE ABLOWITZ-LADIK SYSTEM

被引：0
|
作者：
Killip, Rowan [1 ]
Ouyang, Zhimeng [2 ]
Visan, Monica [1 ]
Wu, Lei [3 ]
机构：
[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA
[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA
[3] Lehigh Univ, Dept Math, Bethlehem, PA 18015 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2025年 / 45卷 / 03期
关键词：
Ablowitz-Ladik system; mKdV; continuum limit; integrable system; Strichartz estimates; DISPERSIVE SCHEMES; CONVERGENCE; EQUATIONS;
D O I：
10.3934/dcds.2024114
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For slowly-varying initial data, solutions to the Ablowitz-Ladik system have been proven to converge to solutions of the cubic Schro<spacing diaeresis>dinger equation. In this paper we show that in the continuum limit, solutions to the Ablowitz-Ladik system with H 1 initial data may also converge to solutions of the modified Korteweg-de Vries equation. . To exhibit this new limiting behavior, it suffices that the initial data is supported near the inflection points of the dispersion relation associated with the Ablowitz-Ladik system. Our arguments employ harmonic analysis tools, Strichartz estimates, and the conservation of mass and energy. Correspondingly, they are applicable beyond the completely integrable models of greatest interest to us.
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页码：821 / 846
页数：26
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