相关论文: Small Numerators Canceling Small Denominators: Is …

We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical…

Power series expansions naturally arise whenever solutions of ordinary differential equations are studied in the regime of perturbation theory. In the case of quasi-periodic solutions the issue of convergence of the series is plagued of the…

We investigate multi-dimensional Hamiltonian systems associated with constant Poisson brackets of hydrodynamic type. A complete list of two- and three-component integrable Hamiltonians is obtained. All our examples possess dispersionless…

Zeroth-order optimization methods are developed to overcome the practical hurdle of having knowledge of explicit derivatives. Instead, these schemes work with merely access to noisy functions evaluations. One of the predominant approaches…

We discuss control of low-dimensional systems which, when uncontrolled, are integrable in the Hamiltonian sense. The controller targets an exact solution of the system in a region where the uncontrolled dynamics has invariant tori. Both…

We investigate consequences of adding irrelevant (or less relevant) boundary operators to a (1+1)-dimensional field theory, using the Ising and the boundary sine-Gordon model as examples. In the integrable case, irrelevant perturbations are…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

Brief introduction to the discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation…

The problem of finding superintegrable Hamiltonians and their integrals of motion can be reduced to solving a series of compatibility equations that result from the overdetermination of the commutator or Poisson bracket relations. The…

This paper reconsiders finite variable reductions of the universal Whitham hierarchy of genus zero in the perspective of dispersionless Hirota equations. In the case of one-variable reduction, dispersionless Hirota equations turn out to be…

We reconsider the fundamental problem of coarse-graining infinite-dimensional Hamiltonian dynamics to obtain a macroscopic system which includes dissipative mechanisms. In particular, we study the thermodynamical implications concerning…

We study a regression model with a huge number of interacting variables. We consider a specific approximation of the regression function under two ssumptions: (i) there exists a sparse representation of the regression function in a…

Multi-symplectic integrators are typically regarded as a discretization of the Hamiltonian partial differential equations. This is due to the fact that, for generic finite-dimensional Hamiltonian systems, there exists only one independent…

Supersymmetrical quantum--mechanical system is consider in the case of d=2. The problem of addition of the lower level to spectrums of matrix and scalar components of d=2 SUSY Hamiltonian is investigated. It is shown that in the case, the…

We consider several Hamiltonian systems perturbed by external agents, that preserve their Hamiltonian structure. We investigate the corrections to the canonical statistics resulting from coupling such systems with possibly large but finite…

High-order virtual excitations play an important role in microscopic models of nuclear reactions at intermediate energies. However, the factorial growth of their complexity has prevented their consistent inclusion in ab initio many-body…

In \textit{SIGMA} \textbf{17} (2021), 091, 12 p.p.\ we have presented an integrable system with a negative time variable number for the Davey-Stewartson hierarchy. Here we develop this approach to construct an integrable equation with a…

Dependable numerical results from long-time simulations require stable numerical integration schemes. For Hamiltonian systems, this is achieved with symplectic integrators, which conserve the symplectic condition and exactly solve for the…

Recently we have studied the Bloch effective Hamiltonian approach to bound states in 2+1 dimensional gauge theories. Numerical calculations were carried out to investigate the vanishing energy denominator problem. In this work we study…

This paper studies the deflation algorithm when applied to estimate a low-rank symmetric spike contained in a large tensor corrupted by additive Gaussian noise. Specifically, we provide a precise characterization of the large-dimensional…