All coboundary Lie bialgebras and their corresponding Poisson–Lie structures are constructed for the oscillator algebra generated by {N,A+, A−,M}. Quantum oscillator algebras are derived from these bialgebras by using the Lyakhovsky and Mudrov formalism and, for some cases, quantizations at both algebra and group levels are obtained, including their universal R–matrices.

It is possible to construct representations of the Lorentz group using four-dimensional harmonic oscillators. This allows us to construct threedimensional wave functions with the usual rotational symmetry for space-like coordinates and one-dimensional wave function for time-like coordinate. It is then possible to construct a representation of the Poincaré group for a massive particles having th...

All coboundary Lie bialgebras and their corresponding Poisson–Lie structures are constructed for the oscillator algebra generated by {N,A+, A−,M}. Quantum oscillator algebras are derived from these bialgebras by using the Lyakhovsky and Mudrov formalism and, for some cases, quantizations at both algebra and group levels are obtained, including their universal R–matrices.

In this paper, a new analytical approach has been presented for solving strongly nonlinear oscillator problems. Iteration perturbation method leads us to high accurate solution. Two different high nonlinear examples are also presented to show the application and accuracy of the presented method. The results are compared with analytical methods and with the numerical solution using Runge-Kutta m...

C λ-extended oscillator algebras, generalizing the Calogero-Vasiliev algebra , where C λ is the cyclic group of order λ, have recently proved very useful in the context of supersymmetric quantum mechanics and some of its variants. Here we determine the spectrum generating algebra of the C λ-extended oscillator. We then construct its coherent states, study their nonclassical properties, and comp...

C λ-extended oscillator algebra and parasupersymmetric quantum mechanics Abstract The C λ-extended oscillator algebra is generated by {1, a, a † , N, T }, where T is the generator of the cyclic group C λ of order λ. It can be realized as a generalized deformed oscillator algebra (GDOA). Its unirreps can thus be easily exhibited using the representation theory of GDOAs and their carrier space sh...

We define the concept of a momentum map for supersymplectic supervectorspaces, and prove the super version of a well-known variation of Noether’s theorem from classical symplectic mechanics. We then characterize the largest supermatrix group that admits a momentum map for the one dimensional supersymmetric harmonic oscillator. It is the identity component of the intersection of the orthosymplec...

Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...