Related papers: Fifty Years of KdV: An Integrable System
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…
In this note we construct asymptotically Lifshitz spacetimes in the Chern-Simons formulation of three dimensional higher spin gravity and relate the resulting theories to integrable systems which are elements of the KdV hierarchy.
We review the status of integrable models from the point of view of their dynamics and integrability conditions. Some integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the…
We show a surprising connection between known integrable Hamiltonian systems with quartic potential and the stationary flows of some coupled KdV systems related to fourth order Lax operators. In particular, we present a connection between…
The contributions of Sophya Kowalewski to the integrability theory of the equations for the heavy top extend to a larger class of Hamiltonian systems on Lie groups; this paper explains these extensions, and along the way reveals further…
Reductions of the KP-Whitham system, namely the (2+1)-dimensional hydrodynamic system of five equations that describes the slow modulations of periodic solutions of the Kadomtsev-Petviashvili (KP) equation, are studied. Specifically, the…
Simple semitoric systems were classified about ten years ago in terms of a collection of invariants, essentially given by a convex polygon with some marked points corresponding to focus-focus singularities. Each marked point is endowed with…
A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
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…
This paper is devoted to the study of some connections between coadjoint orbits in infinite dimensional Lie algebras, isospectral deformations and linearization of dynamical systems. We explain how results from deformation theory,…
This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…
In this paper we consider the possibility to use numerical simulations for a computer assisted analysis of integrability of dynamical systems. We formulate a rather general method of recovering the obstruction to integrability for the…
A time-dependent completely integrable Hamiltonian system is quantized with respect to time-dependent action-angle variables near an instantly compact regular invariant manifold. Its Hamiltonian depends only on action variables, and has a…
Learning a dynamical system from input/output data is a fundamental task in the control design pipeline. In the partially observed setting there are two components to identification: parameter estimation to learn the Markov parameters, and…
The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable…
We extend Halphen's theorem which characterizes the solutions of certain $n$th-order differential equations with rational coefficients and meromorphic fundamental systems to a first-order $n \times n$ system of differential equations. As an…
Integrability in string/field theories is known to emerge when considering dynamics in the moduli space of physical theories. This implies that one has to look at the dynamics with respect to unusual time variables like coupling constants…
A study of harmonic maps into Lie groups as a generalisation of the study of other well-known integrable systems, particularly the Toda and self-dual Chern Simons theories.
The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse…