Exact solutions of nonlinear differential equations are of great importance to the theory and
practice of complex systems. The main point of this review article is to discuss a specific …

We present a comprehensive review of the discrete Boussinesq equations based on their
three-component forms on an elementary quadrilateral. These equations were originally …

This book on integrable systems and symmetries presents new results on applications of
symmetries and integrability techniques to the case of equations defined on the lattice. This …

In this paper an approach to generate multi-dimensionally consistent $ N $-component
systems is proposed. The approach starts from scalar multi-dimensionally consistent …

In this paper, we investigate local and nonlocal reductions of a discrete negative order
Ablowitz–Kaup–Newell–Segur equation. By the bilinearization reduction method, we …

This paper investigates the integrability of a generalized seventh-order Korteweg–de Vries
equation arising in fluids and plasmas. By means of singularity structure analysis, it is …

In this paper, we construct a Grassmann extension of a Yang-Baxter map which first
appeared in the work of Kouloukas and Papageorgiou [J. Phys. A: Math. Theor. 42, 404012 …

Cauchy matrix approach for the discrete Ablowitz–Kaup–Newell–Segur equations is
reconsidered, where two “proper” discrete Ablowitz–Kaup–Newell–Segur equations and two …

In this paper, an iterative learning control problem is addressed for a class of parabolic
partial difference systems. Several discrete D-type iterative learning control algorithms with …

In this paper we prove that the trapezoidal $ H^{4} $ and the $ H^{6} $ families of quad-
equations are Darboux integrable by constructing their first integrals. This result explains …