New exact solutions of two-dimensional integrable generalizations of Kaup-Kuperschmidt and Sawada-Kotera equations via the $\bar\partial$-dressing method

TL;DR

This paper develops exact solutions for 2+1-dimensional integrable generalizations of Kaup-Kuperschmidt and Sawada-Kotera equations using the $arullstopackslashpartial$-dressing method, including solutions with functional parameters and periodic solutions.

Contribution

It introduces a novel application of the $arullstopackslashpartial$-dressing method to these higher-dimensional integrable equations, providing explicit solutions.

Findings

Constructed solutions with functional parameters

Derived periodic solutions

Extended integrability analysis to 2+1 dimensions

Abstract

The 2+1-dimensional integrable generalization of Kaup-Kuperschmidt and Sawada-Kotera equations are studied by $\bar\partial$-dressing method of Zakharov and Manakov. The solutions with functional parameters and periodic solutions are constructed.