Related papers: Systematic method of generating new integrable sys…
In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse…
A multilayered particle is illuminated by plane acoustic or electromagnetic waves of one or several frequencies. We consider the inverse scattering problem for the identification of the layers and of the refraction coefficients of the…
Identifying changes in a pair of 3D aerial LiDAR point clouds, obtained during two distinct time periods over the same geographic region presents a significant challenge due to the disparities in spatial coverage and the presence of noise…
Implicit Neural Representations (INRs) provide a powerful continuous framework for modeling complex visual and geometric signals, but spectral bias remains a fundamental challenge, limiting their ability to capture high-frequency details.…
We survey recent work that relates Pitman's transformation to a variety of classical integrable systems, including the box-ball system, the ultra-discrete and discrete KdV equations, and the ultra-discrete and discrete Toda lattice…
We present a wide class of differential systems in any dimension that are either integrable or complete integrable. In particular, our result enlarges a known family of planar integrable systems. We give an extensive list of examples that…
A linearizable version of multidimensional system of $n$-wave type nonlinear PDEs is proposed. This system is derived using the spectral representation of its solution via the procedure similar to the dressing method for the ISTM-integrable…
We introduce integrable multicomponent non-commutative lattice systems, which can be considered as analogs of the modified Gel'fand-Dikii hierarchy. We present the corresponding systems of Lax pairs and we show directly multidimensional…
Using the procedure of the marked point fusion, there are obtained integrable systems with poles in the matrix of the Lax operator order higher than one, considered Hamiltonians, symplectic structure and symmetries of these systems. Also,…
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…
We derive and analyse a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a…
In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…
We reconstruct a rational Lax matrix of size R+1 from its spectral curve (the desingularization of the characteristic polynomial) and some additional data. Using a twisted Cauchy--like kernel (a bi-differential of bi-weight (1-nu,nu)) we…
We formulate and study an integrable model of Nonlinear Schr\"odinger (NLS)-type through its Lax representation, where one of the Lax operators is quadratic and the other has a rational dependence on the spectral parameter. We discuss the…
The Miura transformation plays a crucial role in the study of integrable systems. There have been various extensions of the Miura transformation, which have been used to relate different kinds of integrable equations and to classify the…
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of…
A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based…
This paper presents a novel approach for the identification of linear time-periodic (LTP) systems in continuous time. This method is based on harmonic modeling and consists in converting any LTP system into an equivalent LTI system with…
We define bi-infinite versions of four well-studied discrete integrable models, namely the ultra-discrete KdV equation, the discrete KdV equation, the ultra-discrete Toda equation, and the discrete Toda equation. For each equation, we show…
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…