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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 ...
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 ...
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 ...
Ermakov-Lewis invariants and Reid systems
(2014)
"Reid´s mth-order generalized Ermakov systems of nonlinear coupling constant ? are equivalent to an integrable Emden-Fowler equation. The standard Ermakov-Lewis invariant is discussed from this perspective, and a closed ...
Integrable equations with Ermakov-Pinney nonlinearities and Chiellini damping
(Elsevier, 2015)
"We introduce a special type of dissipative Ermakov-Pinney equations of the form v?? + g(v)v? + h(v) = 0, where h(v) = h0(v) + cv?3 and the nonlinear dissipation g(v) is based on the corresponding Chiellini integrable Abel ...
One-parameter supersymmetric Hamiltonians in momentum space
(2015)
"Recent results on the one-parameter supersymmetric deformation in momentum space by Curtright and Zachos (2014 J. Phys. A: Math. and Theor. 47 145201) are presented in a more general framework following our own papers. ...
Shifted one-parameter supersymmetric family of quartic asymmetric double-well potentials
(2014)
"Extending our previous work (Rosu, Mancas, Chen, Ann.Phys. 343 (2014) 87-102), we define supersymmetric partner potentials through a particular Riccati solution of the form F(x) = (x − c)2 − 1, where c is a real shift ...
Generalized Thomas-Fermi equations as the Lampariello class of Emden-Fowler equations
(Elsevier, 2017)
"A one-parameter family of Emden-Fowler equations defined by Lampariello's parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard ...
One-parameter families of supersymmetric isospectral potentials from Riccati solutions in function composition form
(2014)
"In the context of supersymmetric quantum mechanics, we define a potential through a particular Riccati solution of the composition form (F ◦ f)(x) = F(f(x)) and obtain a generalized Mielnik construction of one-parameter ...
Nongauge bright soliton of the nonlinear Schrödinger (NLS) equation and a family of generalized NLS equations
(2016)
"We present an approach to the bright soliton solution of the nonlinear Schrödinger (NLS) equation from the standpoint of introducing a constant potential term in the equation. We discuss a "nongauge" bright soliton for ...