The IVP for a certain dispersion generalized ZK equation in bi-periodic spaces

TL;DR

This paper proves well-posedness for a dispersion generalized Zakharov-Kutnesov equation in bi-periodic Sobolev spaces, extending understanding of its mathematical properties in periodic settings.

Contribution

It establishes the well-posedness of the Cauchy problem for a generalized ZK equation in bi-periodic Sobolev spaces, with specific regularity conditions.

Findings

Well-posedness results for the dispersion generalized ZK equation.

Conditions on Sobolev space regularity for solutions.

Extension of previous results to bi-periodic domains.

Abstract

We establish well-posedness conclusions for the Cauchy problem associated to the dispersion generalized Zakharov-Kutnesov equation in bi-periodic Sobolev spaces $H^{s}\left(\mathbb{T}^{2}\right)$, $s>(\frac{3}{2}-\frac{1}{2^{\alpha+2}})(\frac{3}{2}-\frac{\beta}{4})$.