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arXiv · 2608.20721

A Parameterization of Small Amplitude KP Finite Gap Solutions via Classical Schottky Uniformization and Persistence of One and Two Gap Solutions

Haoxuan Liu·Zuhong You·Xiaoping Yuan
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Abstract

We develop a parameterization of small amplitude finite gap solutions to the KP equation with prescribed spatial wavenumber vectors using classical Schottky uniformization. This parameterization is suitable for a Lyapunov-Schmidt reduction. Using this parameterization, we prove the persistence, under Hamiltonian perturbations, of periodic one-gap solutions for both KP-I and KP-II and of bi-periodic two-gap solutions for KP-I.

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Haoxuan Liu, Zuhong You, Xiaoping Yuan. 2026-08-21. A Parameterization of Small Amplitude KP Finite Gap Solutions via Classical Schottky Uniformization and Persistence of One and Two Gap Solutions. https://arxiv.org/abs/2608.20721

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