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Riccati-parameter solutions of nonlinear second-order ODEs
(2008)
"It has been proven by Rosu and Cornejo-Pérez [1, 2] that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order ...
A note on Verhulst's logistic equation and related logistic maps
(2010)
"We consider the Verhulst logistic equation and a couple of forms of the corresponding logistic maps. For the case of the logistic equation we show that using the general Riccati solution only changes the initial conditions ...
Transform of Riccati equation of constant coefficients through fractional procedure
(2003)
"We use a particular fractional generalization of the ordinary differential equations that we apply to the Riccati equation of constant coefficients. By this means the latter is transformed into a modified Riccati equation ...
The hyperbolic, the arithmetic and the quantum phase
(2004)
"We develop a new approach of the quantum phase in an Hilbert space of finite dimension which is based on the relation between the physical concept of phase locking and mathematical concepts such as cyclotomy and the ...
Mutually unbiased bases and finite projective planes
(2004)
"It is conjectured that the question of the existence of a set of d+1 mutually unbiased bases in a d-dimensional Hilbert space if d differs from a power of a prime number is intimately linked with the problem of whether ...
Existence of periodic orbits in nonlinear oscillators of Emden-Fowler form
(2016)
"The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is mapped to an Emden-Fowler (EF) equation that is written as an autonomous two-dimensional ODE system for which we provide the phase-space analysis and ...
An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators
(2012)
"We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators ...
Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations
(2013)
"We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in its first kind form have only cubic and quadratic ...
Parametric oscillators from factorizations employing a constant-shifted Riccati solution of the classical harmonic oscillator
(Elsevier, 2011)
"We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the ...
Barotropic FRW cosmologies with Chiellini damping
(2015)
"It is known that barotropic FRW equations written in the conformal time variable can be reduced to simple linear equations for an exponential function involving the conformal Hubble rate. Here, we show that an interesting ...