Related papers: Recursion operators, conservation laws and integra…
A recursion operator is constructed for a new integrable system of coupled Korteweg - de Vries equations by the method of gauge-invariant description of zero-curvature representations. This second-order recursion operator is characterized…
We introduce a suitable notion of integral operators (comprising the fractional Laplacian as a particular case) acting on functions with minimal requirements at infinity. For these functions, the classical definition would lead to divergent…
In this work we develop a general procedure for constructing the recursion operators fro non-linear integrable equations admitting Lax representation. Svereal new examples are given. In particular we find the recursion operators for some…
We consider the recursion operators with nonlocal terms of special form for evolution systems in (1+1) dimensions, and extend them to well-defined operators on the space of nonlocal symmetries associated with the so-called universal Abelian…
Direct and inverse recursion operator is derived for the vacuum Einstein equations for metrics with two commuting Killing vectors that are orthogonal to a foliation by 2-dimensional leaves.
We present a method to obtain symmetries for second-order systems of ordinary difference equations and how to use them to reduce the order. We also introduce a technique of finding conservation laws for such systems.
Integral operators play an important role modeling various physical and biological processes. In this article we consider such a nonlinear integro-differential equation. We study several properties of equilibrium solutions of the operator…
Operators play a substantial role in mathematical formalism of quantum mechanics. However, explicit forms of the operators are usually postulated, based on the intuitive assumptions. In this study, variational principle was applied to the…
We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…
The notion of lacunary infinite numerical sequence is introduced. It is shown that for an arbitrary linear difference operator L with coefficients belonging to the set R of infinite numerical sequences, a criterion (i.e., a necessary and…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
We present a simple novel construction of recursion operators for integrable multidimensional dispersionless systems that admit a Lax pair whose operators are linear in the spectral parameter and do not involve the derivatives with respect…
We derive a tensorial formula for a fourth-order conformally invariant differential operator on conformal 4-manifolds. This operator is applied to algebraic Weyl tensor densities of a certain conformal weight, and takes its values in…
We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N=2 and N=3 containing the equations of shallow water waves and…
An algorithm is constructed which allows to express conserved flows of hyperbolic equations in terms of corresponding conserved densities and to eliminate these flows from conservation laws of hyperbolic equations. The application of this…
We study integro-differential inclusions in Hilbert spaces with operator-valued kernels and give sufficient conditions for the well-posedness. We show that several types of integro-differential equations and inclusions are covered by the…
In this paper, we describe a framework to compute expected convergence rates for residuals based on the Calder\'on identities for general second order differential operators for which fundamental solutions are known. The idea is that these…
Algorithms for the symbolic computation of polynomial conservation laws, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations (DDEs) are presented. The algorithms can be used to test the…
We present a new recursion and Hamiltonian operators for the Viallet equation. This new recursion operator and the recursion operator found in [Theoretical and Mathematical Physics, 167:421--443 (2011), arXiv:1004.5346] satisfy the elliptic…
We determine, by hierarchy, dependencies between higher order linear symmetries which occur when generating them using recursion operators. Thus, we deduce a formula which gives the number of independent generalized symmetries (basis) of…