The purpose of this article is to discuss an algebraic method for studying integrable
differential-difference lattices with two discrete and one continuous independent variables …

We introduce a novel systematic construction for integrable (3+ 1 3+ 1)-dimensional
dispersionless systems using nonisospectral Lax pairs that involve contact vector fields. In …

In the series of recent publications [,,,], we have proposed a novel approach to the
classification of integrable differential/difference equations in three dimensions based on the …

Infinitely many generalized symmetries of a coupled (2+ 1)-dimensional Burgers system are
obtained by means of the formal series symmetry approach. It is found that the generalized …

The article continues the work on the description of integrable nonlinear chains with three
independent variables of the following form $ u^ j_ {n+ 1, x}= u^ j_ {n, x}+ f (u^{j+ 1} _ {n} …

In this paper we consider integrable dispersive chains associated with the so-called'energy
dependent'Schrödinger operator. In a general case multi-component reductions of these …

This paper is devoted to the classification of integrable Davey–Stewartson type equations. A
novel approach based on the requirement that such systems must be generated by a …

We consider the 3D Mikhalev system, ut= wx, uy= wt-uwx+ wux, which has first appeared in
the context of KdV-type hierarchies. Under the reduction w= f (u), one obtains a pair of …

A functional of the solution of the Kadomtsev–Petviashvili II equation maps multi-soliton
solutions onto systems of vertices—structures that are localized around soliton junctions. A …

We continue describing integrable nonlinear chains of the form with three independent
variables on the basis of the existence of a hierarchy of Darboux-integrable reductions. The …