Work

Asymptotics for small data solutions of the Ablowitz-Ladik equation

Year: 2025

Type: article

Abstract: We study the asymptotics for the Ablowitz-Ladik equation. By taking appropriate continuum limits, it can be shown that the behavior of the equation near degenerate frequencies is well approximated by a complex modified Korteweg-de Vries equation. Using this connection, we use the method of space-time resonances to derive a description of the modified scattering behavior of the Ablowitz-Ladik equation, which includes two regions where the solution behaves like a self-similar solution to the complex mKdV equation.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2025075

Author: Gavin Stewart

Institutions: Rutgers, The State University of New Jersey, Arizona State University

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4411164696

FWCI:

Cites: 32

Cited by: 1

Related to: 10