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arXiv · 2303.10496

Asymptotics for small data solutions of the Ablowitz-Ladik equation

Gavin Stewart
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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.

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Gavin Stewart. 2023-03-18. Asymptotics for small data solutions of the Ablowitz-Ladik equation. https://doi.org/10.3934/dcds.2025075

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