The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the
following steps:(1) Lax representation [L, M]= 0;(2) construction of fundamental analytic …

It is known that the initial‐boundary value problem for certain integrable Partial Differential
Equations (PDEs) on the half‐line with integrable boundary conditions can be mapped to a …

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 …

We extend the reduction group method to the Lax-Darboux schemes associated with
nonlinear Schrödinger type equations. We consider all possible finite reduction groups and …

Krichever and Novikov introduced certain classes of infinite dimensional Lie algebras to
extend the Virasoro algebra and its related algebras to Riemann surfaces of higher genus …

In this paper we show that there are explicit Yang–Baxter (YB) maps with Darboux–Lax
representation between Grassman extensions of algebraic varieties. Motivated by some …

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 …

A special class of integrable nonlinear differential equations related to A. III-type symmetric
spaces and having additional reductions are analyzed via the inverse scattering method …

We study a class of integrable nonlinear differential equations related to the A. III-type
symmetric spaces. These spaces are realized as factor groups of the form SU (N)/S (U (N …