Related papers: Recursion Operators for Multidimensional Integrabl…
In this paper we find all complex symmetric weighted composition operators with special conjugations. Then we give spectral properties of these complex symmetric weighted composition operators.
Starting from a $d\times d$ rational Lax pair system of the form $\hbar \partial_x \Psi= L\Psi$ and $\hbar \partial_t \Psi=R\Psi$ we prove that, under certain assumptions (genus $0$ spectral curve and additional conditions on $R$ and $L$),…
This paper discusses the algorithms and implementations of three Mathematica packages for the study of integrability and the computation of closed-form solutions of nonlinear polynomial PDEs. The first package, PainleveTest.m, symbolically…
In this paper we study the Weihrauch complexity of projection operators onto closed subsets of the Euclidean space. We show that some fundamental degrees of the Weihrauch lattice can be characterized in terms of such operators.
This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors…
In this paper, we study design of deep neural networks for tasks of image restoration. We propose a novel style of residual connections dubbed "dual residual connection", which exploits the potential of paired operations, e.g., up- and…
We extend the recursion formula for matrix Bessel functions, which we obtained previously, to superspace. It is sufficient to do this for the unitary orthosymplectic supergroup. By direct computations, we show that fairly explicit results…
An algebraic construction more general and intimately connected with that of Faddeev$^1$, along with its application for generating different classes of quantum integrable models are summarised to complement the recent results of ref. 1 (…
This paper is devoted to the classification of integrable Davey-Stewartson type equations. A list of potentially deformable dispersionless systems is obtained through the requirement that such systems must be generated by a polynomial…
We present examples of Lax-integrable multi-dimensional systems of partial differential equations with higher local symmetries. We also consider Lagrangian deformations of these equations and construct variational bivectors on them.
New quasilocal recursion and Hamiltonian operators for the Krichever-Novikov and the Landau-Lifshitz equations are found. It is shown that the associative algebra of quasilocal recursion operators for these models is generated by a couple…
In this paper we develop a general concept of Lax operators on algebraic curves introduced in [1]. We observe that the space of Lax operators is closed with respect to their usual multiplication as matrix-valued functions. We construct the…
In this paper the notion of an M-th order invariant bilinear differential pairing is introduced and a formal definition is given. If the manifold has an AHS structure, then various first order pairings are constructed. This yields a…
This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes…
X-ray ptychography is a powerful and robust coherent imaging method providing access to the complex object and probe (illumination). Ptychography reconstruction is typically performed using first-order methods due to their computational…
In this paper, we show that many complex patterns, which characterize the decorative style of many artisanal objects, can be generated by the recursive application of only four operators. Each operator is derived from tracing the isolines…
Training Neural ODEs requires backpropagating through an ODE solve. The state-of-the-art backpropagation method is recursive checkpointing that balances recomputation with memory cost. Here, we introduce a class of algebraically reversible…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
The paper continues nlin.SI/0212019 by giving three more examples of using cyclic bases of zero-curvature representations in studies of relation between strong Lax pairs and recursion operators.
We present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^1$-duality estimates.