11 Results Found

It is shown that quantization and superintegrability are not concepts that are inherent to classical Physics alone. Indeed, one may quantize and also detect superintegrability of biological models by means of Noether symmetries. We exemplify the meth...

In this paper, we present the integrable deformations method for a maximally superintegrable system. We alter the constants of motion, and using these new functions, we construct a new system which is an integrable deformation of the initial system....

The determination of the first integrals (FIs) of a dynamical system and the subsequent assessment of their integrability or superintegrability in a systematic way is still an open subject. One method which has been developed along these lines for ho...

We consider the generic quadratic first integral (QFI) of the form $I=K_{ab}(t,q){\dot{q}}^a{\dot{q}}^b+K_a(t,q){\dot{q}}^a+K(t,q)$ and require the condition $dI/dt=0.$ The latter results in a system of partial differential equations which involve the tensors $K_{ab}(t,q)$, $K_a(t,q)$, $K(t$...

In this article, we adopt two kinds of loop algebras corresponding to the Lie algebra $B(0,1)$ to introduce two line spectral problems with different numbers of even and odd superfunctions. Through generalizing the time evolution ${\lambda }_t$ to a polynomial of...

We consider autonomous conservative dynamical systems which are constrained with the condition that the total energy of the system has a specified value. We prove a theorem which provides the quadratic first integrals (QFIs), time-dependent and auton...

In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number $\pi$ . This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of $\pi$ in a base de...

Among the few exactly solvable problems in theoretical physics, the 2D (two-dimensional) Newtonian free fall problem in Euclidean space is perhaps the least known as compared to the harmonic oscillator or the Kepler–Coulomb problems. The aim of...

The $4\times 4$ trace-free complex matrix set is introduced in this study. By using it, we are able to create a novel soliton hierarchy that is reduced to demonstrate its bi-Hamiltonian structure. Additionally, we give the Darboux matrix T, whose eleme...

We study an interesting superization problem of integrable nonlinear dynamical systems on functional manifolds. As an example, we considered a quantum many-particle Schrödinger–Davydov model on the axis, whose quasi-classical reduction pro...

Lithofacies, as an integrated representation of key reservoir attributes including mineral composition and organic matter enrichment, provides crucial geological and engineering guidance for identifying “dual sweet spots” and designing fr...