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

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.

18 pages