Related papers: Linearizability for third order evolution equation…
Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…
For an elliptic curve $E$ defined over the field $\mathbb{C}$ of complex numbers, we classify all translates of elliptic curves in $E^3$ such that the $x$-coordinates satisfy a linear equation. This classification enables us to establish a…
Several classes of systems of evolution equations with one or two vector unknowns are considered. We investigate also systems with one vector and one scalar unknown. For these classes all equations having the simplest higher symmetry are…
We show some classes of higher order partial difference equations admitting a zero-curvature representation and generalizing lattice potential KdV equation. We construct integrable hierarchies which, as we suppose, yield generalized…
The symmetry approach to the classification of evolution integrable partial differential equations (see, for example \cite{MikShaSok91}) produces an infinite series of functions, defined in terms of the right hand side, that are conserved…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
Symmetries for wave equation with additional conditions are found. Some conditions yield infinite-dimensional symmetry algebra for the nonlinear equation. Ansatzes and solutions corresponding to the new symmetries were constructed.
The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…
Discusses several integrability tests for nonlinear evolution equations.
This paper is centred on solving differential equations by symmetry groups for first order ODEs and is in response to Starrett (2007). It also explores the possibility of averting the assumptions by Olver (2000) that, in practice finding…
We propose a new method for solution of the integrability problem for evolutionary differential-difference equations of arbitrary order. It enables us to produce necessary integrability conditions, to determine whether a given equation is…
We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and…
We investigate the local integrability and linearizability of three dimensional Lotka-Volterra equations at the origin. Necessary and sufficient conditions for both integrability and linearizability are obtained for (1,-1,1), (2,-1,1) and…
The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a…
We prove that any homogeneous order one solution to 3-d nondivergence elliptic equations must be linear.
We develop a theory of loops with involution. On this basis we define a Cayley-Dickson doubling on loops, and use it to investigate the lattice of varieties of loops with involution, focusing on properties that remain valid in the…
Point transformations of the 3-rd order ordinary differential equations are considered. Special classes of ordinary differential equations that are invariant under the general point transformations are constructed.
We expand our group classification of quasilinear evolution equations (Acta Appl.Math., v.69, 2001) to the case of general evolution equation in one spatial variable. This enables obtaining several new classes of evolution equations with…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…