Work

The modified Korteweg–de Vries limit of the Ablowitz–Ladik system

Year: 2024

Type: article

Abstract: For slowly-varying initial data, solutions to the Ablowitz–Ladik system have been proven to converge to solutions of the cubic Schrödinger 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.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2024114

Authors: Rowan Killip, Zhimeng Ouyang, Monica Visan, Lei Wu

Institutions: University of Chicago, University of California, Los Angeles, Lehigh University

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4402209521

FWCI: 0.657

Cites: 21

Cited by: 1

Related to: 10