Related papers: Integrability test for evolutionary lattice equati…
The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of…
We consider a class of systems of difference equations defined on an elementary quadrilateral of the ${\mathbb{Z}}^2$ lattice, define their eliminable and dynamical variables, and demonstrate their use. Using the existence of infinite…
An evolution equation, arising in the study of the Dynamical Systems Method (DSM) for solving equations with monotone operators, is studied in this paper. The evolution equation is a continuous analog of the regularized Newton method for…
We suggest an approach for description of integrable cases of the Abel equations. It is based on increasing of the order of equations up to the second one and using equivalence transformations for the corresponding second-order ordinary…
We study differential-difference equation of the form $t_{x}(n+1)=f(t(n),t(n+1),t_x(n))$ with unknown $t=t(n,x)$ depending on $x$, $n$. The equation is called Darboux integrable, if there exist functions $F$ (called an $x$-integral) and $I$…
Determining if an (1+1)-differential-difference equation is integrable or not (in the sense of possessing an infinite number of symmetries) can be reduced to the study of the dependence of the equation on the lattice points, according to…
For systems of evolutionary partial differential equations the tau-structure is an important notion which originated from the deep relation between integrable systems and quantum field theories. We show that, under a certain non-degeneracy…
A method for constructing evolution equations admitting a master symmetry is proposed. Several examples illustrating the method are presented. It is also noted that for certain evolution equations master symmetries can be useful for…
A uniform gradient for functions u which satisfy a system of N second-order partial differential inequalities is given in this paper. Some structure conditions are given for the coefficients of the matrices of second-order terms and of…
We prove two results concerning an Ulam-type stability problem for homomorphisms between lattices. One of them involves estimates by quite general error functions; the other deals with approximate (join) homomorphisms in terms of certain…
We extend the integrability analysis for scalar evolution equations of type $$u_t=u_m+f(u,u_1,...,u_{m-1})$$ from the case that the right hand side is a $\lambda$-homogeneous formal power series to the case that it is a nonhomogeneous…
We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…
In this work we propose a mechanism for converting the spectral problem of vertex models transfer matrices into the solution of certain linear partial differential equations. This mechanism is illustrated for the…
Every orthonomic system of partial differential equations is known to possess a finite number of integrability conditions sufficient to ensure the validity of all. Herewith we offer an efficient algorithm to construct a sufficient set of…
In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
The combination of uninterpreted function symbols and universal quantification occurs in many applications of automated reasoning, for example, due to their ability to reason about arrays. Yet the satisfiability of such formulas is, in…
In this short note we give incremental algorithms for the following lattice problems: finding a basis of a lattice, computing the successive minima, and determining the orthogonal decomposition. We prove an upper bound for the number of…
Obstacles to integrability sometimes hamper the standard Normal Form analysis of perturbed integrable evolution equations. One is then forced to account for them by the Normal Form, which is the dynamical equation obeyed by the zero-order…
We consider solutions of the Cauchy problem for semilinear equations with (possibly) different L\'evy operators. We provide various results on their convergence under the assumption that symbols of the involved operators converge to the…