# Modified Zakharov-Kuznetsov equation on rectangles

## TL;DR

This paper investigates the initial-boundary value problem for the modified Zakharov-Kuznetsov equation on rectangles, addressing the challenges posed by the critical nonlinear power and analyzing the solutions' existence, uniqueness, and long-term behavior.

## Contribution

It provides new results on existence, uniqueness, and asymptotic behavior for solutions of the modified Zakharov-Kuznetsov equation on bounded rectangles, handling the critical nonlinear power.

## Key findings

- Proved existence of solutions under certain conditions
- Established uniqueness of solutions
- Analyzed asymptotic behavior of solutions

## Abstract

Initial-boundary value problem for the modified Zakharov-Kuznetsov equation posed on a bounded rectangle is considered. The main difficulty is the critical power in nonlinear term. The results on existence, uniqueness and asymptotic behavior of solutions are presented.