We review two concepts directly related to the Lax representations of integrable systems:
Darboux transformations and recursion operators. We present an extensive list of integrable …

In this paper, we construct Yang–Baxter (YB) maps using Darboux matrices which are
invariant under the action of finite reduction groups. We present six-dimensional YB maps …

A CLASSIFICATION OF AUTOMORPHIC LIE ALGEBRAS ON COMPLEX TORI Page 1
Proceedings of the Edinburgh Mathematical Society: page 1 of 43 doi:10.1017/S0013091524000324 …

We study automorphic Lie algebras and their applications to integrable systems.
Automorphic Lie algebras are a natural generalisation of celebrated Kac-Moody algebras to …

In this paper, we derive new two-component integrable differential difference and partial
difference systems by applying a Lax-Darboux scheme to an operator formed from an 𝔰𝔩 3 …

We show how the recently again discussed N-point Witt, Virasoro, and affine Lie algebras
are genus zero examples of the multipoint versions of Krichever–Novikov-type algebras as …

In the paper we develop the dressing method for the solution of the two-dimensional
periodic Volterra system with a period N. We derive soliton solutions of arbitrary rank k and …

We study automorphic Lie algebras using a family of evaluation maps parametrised by the
representations of the associative algebra of functions. This provides a descending chain of …

An automorphic Lie algebra is a Lie algebra of certain invariants, initially arising in the
theory of integrable systems, or more specifically, in the context of algebraic reduction of Lax …

Abstract Automorphic Lie Algebras arise in the context of reduction groups introduced in the
late 1970s [35] in the field of integrable systems. They are subalgebras of Lie algebras over …