Related papers: Integrability ex machina
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…
Integrable systems have provided various insights into physical phenomena and mathematics. The way of constructing many-body integrable systems is limited to few ansatzes for the Lax pair, except for highly inventive findings of conserved…
In this paper we continue the description of the possibilities to use numerical simulations for mathematically rigorous computer assisted analysis of integrability of dynamical systems. We sketch some of the algebraic methods of studying…
Two simple ways to identify and explain fake Lax pairs are provided. The two methods are complementary, one involves finding a gauge transformation which can be used to remove the associated nonlinear system's dependent variable(s) from a…
In paper by I.T. Habibullin and our joint paper the algorithm for classification of integrable equations with three independent variables was proposed. This method is based on the requirement of the existence of an infinite set of Darboux…
We define observability and detectability for linear switching systems as the possibility of reconstructing and respectively of asymptotically reconstructing the hybrid state of the system from the knowledge of the output for a suitable…
We systematically derive the Lax pair formulation for both discrete and continuum integrable classical theories with consistent boundary conditions.
In a previous article [N. Delice, F.W. Nijhoff and S. Yoo-Kong, J. Phys. A: Math. Theor. 48(3) (2015), 035206] a novel class of elliptic Lax pairs for integrable lattice equations was introduced. The present article proposes a…
We give a short summary of our recent works on the classical integrable structure of two-dimensional non-linear sigma models defined on squashed three-dimensional spheres. There are two descriptions to describe the classical dynamics, 1)…
A new ansatz is presented for a Lax pair describing systems of particles on the line interacting via (possibly nonsymmetric) pairwise forces. Particular cases of this yield the known Lax pairs for the Calogero-Moser and Toda systems, as…
We consider systems composed of an unbounded number of uniformly designed linear hybrid automata, whose dynamic behavior is determined by their relation to neighboring systems. We present a class of such systems and a class of safety…
Studying the reliability of complex systems using machine learning techniques involves facing a series of technical and practical challenges, ranging from the intrinsic nature of the system and data to the difficulties in modeling and…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
In this article, we present an automated approach that would test for and discover the interoperability of CAD systems based on the approximately-invariant shape properties of their models. We further show that exchanging models in standard…
While reachability analysis is one of the most promising approaches for formal verification of dynamic systems, a major disadvantage preventing a more widespread application is the requirement to manually tune algorithm parameters such as…
We show how the superintegrability of certain systems can be deduced from the presence of multiple parameters in the rational Lax matrix representation. This is also related to the fact that such systems admit a separation of variables in…
The relation between integrable systems and algebraic geometry is known since the XIXth century. The modern approach is to represent an integrable system as a Lax equation with spectral parameter. In this approach, the integrals of the…
Precisely modeling complex systems like cyber-physical systems is challenging, which often render model-based system verification techniques like model checking infeasible. To overcome this challenge, we propose a method called LAR to…
This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the…
We formulate the discovery of Lax integrability of Hamiltonian dynamical systems as a symbolic regression problem, which, loosely speaking, seeks to maximize the compatibility between a pair of Lax operators and the known Hamiltonian of the…