Note on 2d binary operadic harmonic oscillator

Abstract

It is explained how the time evolution of operadic variables may be introduced by using the operadic Lax equation. As an example, a 2-dimensional binary operadic Lax representation for the harmonic oscillator is constructed.

Note on 2d binary operadic harmonic oscillator 1

“…Research was in part supported by the Estonian Science Foundation, Grant ETF 6912. More expanded version of the present paper is presented in [9].…”

Jacobi operators of quantum counterparts of three-dimensional real Lie algebras over the harmonic oscillator

“…In particular, the time evolution of the operadic variables may be given by the operadic Lax equation. In [5,6,8], the low-dimensional binary operadic Lax representations for the harmonic oscillator were constructed. In [7] it was shown how the operadic Lax representations are related to the conservation of energy.…”

Quantum counterparts of VIIα, IIIα=1, VIα≠1over the harmonic oscillator in semiclassical approximation

“…In particular, the time evolution of the operadic variables may be given by the operadic Lax equation. In [5,6,7], the low-dimensional binary operadic Lax representations for the harmonic oscillator were constructed. In [8] it was shown how the operadic Lax representations are related to the conservation of energy.…”