Darboux transformation is an efficient method for solving different nonlinear partial
differential equations. In this paper, on the basis of a Lie super-algebras, a generalized …

A supertrace identity on Lie superalgebras is established. It provides a tool for constructing
super-Hamiltonian structures of zero curvature equations associated with Lie superalgebras …

An algorithm to generate integrable systems is extended to the super case. Some new
examples of superextensions of integrable systems are illustrated. We also generalize the …

There are two known integrable N= 2 space supersymmetric extensions of the KdV
equation. Both can be written as Hamiltonian systems with a common Poisson structure …

Based on the constructed new Lie super-algebra from OSP (2, 2), the super bi-Hamiltonian
structure of a new super AKNS hierarchy is obtained by making use of super-trace identity …

We propose a super Lax type equation based on a certain class of Lie superalgebra as a
supersymmetric extension of generalized (modified) KdV hierarchy. We are able to construct …

We will discuss how to generate integrable couplings from zero curvature equations
associated with matrix spectral problems. The key elements are matrix loop algebras …

This report is concerned with Hamiltonian structures of classical and super soliton
hierarchies. In the classical case, basic tools are variational identities associated with …

We present some nonlocal integrable systems by using the Ablowitz–Musslimani nonlocal
reductions. We first present all possible nonlocal reductions of nonlinear Schrödinger (NLS) …

We present nonlocal integrable reductions of the Fordy–Kulish system of nonlinear
Schrodinger equations and the Fordy system of derivative nonlinear Schrodinger equations …