相关论文: Extension of the Adler-Bobenko-Suris classificatio…
We present the new extended supersymmetrization of the Nonlinear Schrodinger Equation by introducing two superbosons fields with the different gradation. Our model is different from this considered by Toppan and in the reduced case…
In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable…
We study different extended formulations for the set $X = \{x\in\mathbb{Z}^n \mid Ax = Ax^0\}$ in order to tackle the feasibility problem for the set $X_+=X \cap \mathbb{Z}^n_+$. Here the goal is not to find an improved polyhedral…
The irreducible modules of the 2-cycle permutation orbifold models of lattice vertex operator algebras of rank 1 are classified, the quantum dimensions of irreducible modules and the fusion rules are determined.
A generalization of the Yang-Baxter equation is proposed. It enables to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit…
Based on the work by Smirnov and Zeitlin, we study a simple realization of the matrix construction of the affine Jacobi varieties. We find that the realization is given by a classical integrable model, the extended Lotka-Volterra lattice.…
We consider differential-difference equations that determine the continuous symmetries of discrete equations on the triangular lattice. It is shown that a certain combination of continuous flows can be represented as a scalar evolution…
We address the problem of classification of integrable differential-difference equations in 2+1 dimensions with one/two discrete variables. Our approach is based on the method of hydrodynamic reductions and its generalisation to dispersive…
We consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions we show that wave-like solutions exist when obstacles (characterized by "holes") are present in the…
This paper proposes a method for identifying and classifying integrable nonlinear equations with three independent variables, one of which is discrete and the other two are continuous. A characteristic property of this class of equations,…
A straightforward algorithm for the symbolic computation of higher-order symmetries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the…
We present an integrability test for discrete equations on the square lattice, which is based on the existence of a generalized symmetry. We apply this test to a number of equations obtained in different recent papers. As a result we prove…
The class of ordinary linear constant coefficient differential equations is naturally embedded into a wider class by associating differential equations to algebraic curves.
Relativistic complex Burgers-Schr\"odinger and Nonlinear Schr\"odinger equations are constructed. In the non-relativistic limit they reduce to the standard Burgers and NLS equations respectively and are integrable at any order of…
Two extension problems are solved. First, the class of locally matricial algebras over an arbitrary field is closed under extensions. Second, the class of locally finite dimensional semisimple algebras over a fixed field is closed under…
Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most…
We prove an algebraic canonicity theorem for normal LE-logics of arbitrary signature, in a generalized setting in which the non-lattice connectives are interpreted as operations mapping tuples of elements of the given lattice to closed or…
We investigate computability in the lattice of equivalence relations on the natural numbers. We mostly investigate whether the subsets of appropriately defined subrecursive equivalence relations -for example the set of all polynomial-time…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
Structure of certain simple $\mathcal{W}$-algebras assocated with the Deligne exceptional Lie algebras and non-admissible levels are described as the {\it simple current extensions} of certain vertex operator algebras. As an application,…