Based on the stationary zero-curvature equation and the Lenard recursion equations, we
derive the coupled modified Korteweg–de Vries (cmKdV) hierarchy associated with a 3× 3 …

In this paper, we consider the robust inverse scattering method for the Ablowitz–Ladik (AL)
equation on the non-vanishing background, which can be used to deal with arbitrary-order …

We develop a theory of Darboux transformations for CMV matrices, canonical
representations of the unitary operators. In perfect analogy with their self-adjoint version–the …

This paper studies the discrete Ablowitz–Ladik equation via the Riemann-Hilbert (RH)
approach. By its matrix spectral problem and Lax pair, the Jost solution and the reflection …

The study of set-theoretic solutions of the Yang-Baxter equation, also known as Yang-Baxter
maps, is historically a meeting ground for various areas of mathematics and mathematical …

The study of the set-theoretic solutions of the reflection equation, also known as reflection
maps, is closely related to that of the Yang-Baxter maps. In this work, we construct reflection …

Based on the Lenard recursion equations and the stationary zero-curvature equation, we
derive the coupled Sasa–Satsuma hierarchy, in which a typical number is the coupled Sasa …

Based on the Lenard recursion equations, we derive the Lax pair for the hierarchy of
coupled long wave–short wave resonance equations, in which the first nontrivial member is …

Based on the characteristic polynomial of Lax matrix for the hierarchy of coupled Toda
lattices associated with a 3× 3 3\times3 discrete matrix spectral problem, we introduce a …

Based on the Lenard recursion relation and the zero-curvature equation, we derive a
hierarchy of long wave-short wave type equations associated with the 3× 3 matrix spectral …