Related papers: Generating Finite Dimensional Integrable Nonlinear…
We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian)…
Integrable systems appeared in physics long ago at the onset of classical dynamics with examples being Kepler's and other famous problems. Unfortunately, the majority of nonlinear problems turned out to be nonintegrable. In accelerator…
In this paper, we consider the systems with trajectories originating in the nonnegative orthant becoming nonnegative after some finite time transient. First we consider dynamical systems (i.e., fully observable systems with no inputs),…
We propose a periodically driven system whose dimensionality is an emergent property that can be tunable, thus enables us to realize not only many-body phases with arbitrary dimensions, but also phase transitions, instead of crossovers,…
A collisionless kinetic plasma model may often be cast as an infinite-dimensional noncanonical Hamiltonian system. I show that, when this is the case, the model can be discretized in space and particles while preserving its Hamiltonian…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
We propose a lattice model, in both one- and multidimensional versions, which may give rise to matching conditions necessary for the generation of solitons through the second-harmonic generation. The model describes an array of linearly…
Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the…
The collective dynamics of nonlinear electron waves in an one-dimensional degenerate electron gas is treated using the Lagrangian fluid approach. A new class of solutions with a nontrivial space and time dependence is derived. Both…
In this paper, we consider a generalized second order nonlinear ordinary differential equation of the form $\ddot{x}+(k_1x^q+k_2)\dot{x}+k_3x^{2q+1}+k_4x^{q+1}+\lambda_1x=0$, where $k_i$'s, $i=1,2,3,4$, $\lambda_1$ and $q$ are arbitrary…
There is developed a differential-algebraic approach to studying the representations of commuting differentiations in functional differential rings under nonlinear differential constraints. An example of the differential ideal with the only…
This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of…
In recent papers by the authors (S.~Motonaga and K.~Yagasaki, Obstructions to integrability of nearly integrable dynamical systems near regular level sets, submitted for publication, and K.~Yagasaki, Nonintegrability of nearly integrable…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…
This paper aims to show that there exist non-symmetry constraints which yield integrable Hamiltonian systems through nonlinearization of spectral problems of soliton systems, like symmetry constraints. Taking the AKNS spectral problem as an…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
The long-term behaviour of solutions to a model for acoustic-structure interactions is addressed; the system is comprised of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of…
The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…