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arXiv · 2609.14158

On Periodic Solutions of the Zakharov-Rubenchik System

Yeison Alejandro Gómez Hernández·Juan Carlos Cordero Ceballos
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Abstract

We study the one-dimensional Zakharov-Rubenchik system with periodic initial conditions. This system models the interaction of low-frequency waves with high-frequency waves in different physical phenomena. Using semigroup theory, we prove the global well-posedness of the associated linear equation in $H^q(\mathbb{T})\times H^s(\mathbb{T})\times H^{s+1}(\mathbb{T})$, $q,s \in \mathbb{R}$. Subsequently, we consider the modified Zakharov-Rubenchik system and, by means of a change of variables and the Banach Fixed Point Theorem, we obtain local well-posedness in the space $H^s(\mathbb{T})\times H^s(\mathbb{T})\times H^{s+1}(\mathbb{T})$, $s>3/2$.

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Yeison Alejandro Gómez Hernández, Juan Carlos Cordero Ceballos. 2026-09-12. On Periodic Solutions of the Zakharov-Rubenchik System. https://arxiv.org/abs/2609.14158

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