Related papers: Recursion operator for a system admitting Lax repr…
We construct an operator system generated by $4$ operators that is not hyperrigid, although all restrictions of irreducible representations have the unique extension property.
Identification of nonlinear dynamic systems remains a significant challenge across engineering. This work suggests an approach based on Bayesian filtering to extract and identify the contribution of an unknown nonlinear term in the system…
We describe the representation of arbitrary density operators in terms of expectation values of simple projection operators. Two representations are presented which yield non--recursive schemes for experimentally determining the density…
We construct a recursion operator for the family of Narita-Itoh-Bogoyavlensky infinite lattice equations using its Lax presentation and present their mastersymmetries and bi-Hamiltonian structures. We show that this highly nonlocal…
In this paper, we construct a new Lax operator for the elliptic Calogero-Moser model with N=2. The nondynamical r-matrix structure of this Lax operator is also studied . The relation between our Lax operator and the Lax operator given by…
A systematic method for the design of linear residual generators for combined fault detection and estimation in nonlinear systems is developed. The proposed residual generator is a linear functional observer built for an extended system…
We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the…
We discuss the dispersionless Boussinesq type equation, which is equivalent to the Benney-Lax equation, being a system of equations of hydrodynamical type. This equation was discussed in <http://dx.doi.org/doi:10.1088/0305-4470/27/1/013>.…
This paper is devoted to introduce the non linear reconstruction operator PPH on non uniform grids. We define this operator and we study its main properties such as reproduction of polynomials of second degree, approximation order and…
This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating…
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.
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
It is well known that the Laplace cascade method is an effective tool for constructing solutions to linear equations of hyperbolic type, as well as nonlinear equations of the Liouville type. The connection between the Laplace method and…
We show that boundary contributions of BCFW recursions can be interpreted as the form factors of some composite operators which we call 'boundary operators'. The boundary operators can be extracted from the operator product expansion of…
A super-algebraic formulation of the N=2 supersymmetric unconstrained matrix (k|n,m)-MGNLS hierarchies (nlin.SI/0201026) is established. Recursion operators, fermionic and bosonic symmetries as well as their superalgebra are constructed for…
By the recursion operator of the Kaup-Newell hierarchy we construct the relativistic derivative NLS (RDNLS) equation and the corresponding Lax pair. In the nonrelativistic limit $c \rightarrow \infty$ it reduces to DNLS equation and…
We choose a complete set of square integrable functions as basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent wave operator is tridiagonal and…
We describe a general method of constructing nonlocal recursion operators for symmetries of PDEs. As an example, the cotangent equation to the 3D rdDym equation $u_{yt} = u_xu_{xy} - u_yu_{xx}$ for which two mutually inverse operators are…
We study point and higher symmetries for the hydrodynamic-type systems with two independent variables $t$ and $x$ with and without explicit dependence of the equations on $t,x$. We consider those systems which possess an…
We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators which reproduce certain parts of the…