A relation between semi-direct sums of Lie algebras and integrable couplings of continuous
soliton equations is presented, and correspondingly, a feasible way to construct integrable …

We construct integrable PT-symmetric nonlocal reductions for an integrable hierarchy
associated with the special orthogonal Lie algebra $\operatorname {so}(3,\mathbb {R}) …

A relation between semidirect sums of Lie algebras and integrable couplings of lattice
equations is established, and a practicable way to construct integrable couplings is further …

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By enlarging the associated matrix spectral problems, two specific classes of
multicomponent integrable couplings of the physically important vector AKNS soliton …

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

The discrete variational identity under general bilinear forms on semi-direct sums of Lie
algebras is established. The constant γ involved in the variational identity is determined …

This is an introductory report concerning our recent research on Hamiltonian structures. We
will discuss variational identities associated with continuous and discrete spectral problems …

The Darboux transformation method with 4× 4 spectral problem has more complexity than
2× 2 and 3× 3 spectral problems. In this paper, we start from a new discrete spectral problem …

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