Asymptotics for small data solutions of the Ablowitz-Ladik equation
Analysis of PDEs
2025-08-01 v2
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.
Keywords
Cite
@article{arxiv.2303.10496,
title = {Asymptotics for small data solutions of the Ablowitz-Ladik equation},
author = {Gavin Stewart},
journal= {arXiv preprint arXiv:2303.10496},
year = {2025}
}
Comments
60 pages, 1 figure. Updated references