Abstract Writing the Hirota-Satsuma (HS) system of equations in a symmetrical form we find
its local and new nonlocal reductions. It turns out that all reductions of the HS system are …

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 …

The nonlocal symmetry is derived from the known Darboux transformation (DT) of the Hirota-
Satsuma coupled Korteweg-de Vries (HS-cKdV) system, and infinitely many nonlocal …

Integrable systems are usually given in terms of functions of continuous variables (on R⁠), in
terms of functions of discrete variables (on Z⁠), and recently in terms of functions of q …

This paper is devoted to the complete classification of integrable one-component evolution
equations whose field variable takes its values in an associative algebra. The proof that the …

We suggest a direct algorithm for searching the Lax pairs for nonlinear integrable equations.
It is effective for both continuous and discrete models. The first operator of the Lax pair …

Here, noncommutative hierarchies of nonlinear equations are studied. They represent a
generalization to the operator level of corresponding hierarchies of scalar equations, which …

In this paper we discuss the structure of recursion operators. We show that recursion
operators of evolution equations have a nonlocal part that is determined by symmetries and …

. General solution formulas for the KdV and mKdV hierarchies are derived by means of
Banach space techniques both in the scalar and matrix case. A detailed analysis is given of …

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