Two generalized (2+1)-dimensional hierarchies and Darboux transformations

Baiying He and Lili Ma

Abstract

Based on the TAH scheme, we construct the generalized (2+1)- dimensional S-mKdv hierarchy and the generalized (2+1)-dimensional Levi hierarchy, and we also generate their Hamiltonian structures. At last, we also obtain the Darboux transformations of the generalized (2+1)-dimensional Levi hierarchy.