136 citations · 736 across the 109 of their papers we have counts for
17 papers · 1 filter
On the application of the Lindstedt-Poincaré method to the Lotka-Volterra system
Paolo Amore, Francisco M. Fernández
We apply the Lindstedt-Poincaré method to the Lotka-Volterra model and discuss alternative implementations of the approach. By means of an efficient systematic algorithm we obtain…
On the symmetry of three identical interacting particles in a one-dimensional box
Paolo Amore, Francisco M. Fernández
We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group…
-symmetric strings
Paolo Amore, Francisco M. Fernández, Javier Garcia +1
We study both analytically and numerically the spectrum of inhomogeneous strings with -symmetric density. We discuss an exactly solvable model of -symme…
On the eigenvalues of some nonhermitian oscillators
Francisco M. Fern/'andez, Javier Garcia
We consider a class of one-dimensional nonhermitian oscillators and discuss the relationship between the real eigenvalues of PT-symmetric oscillators and the resonances obtained by…
Comment on: 'A simple analytical expression for bound state energies for an attractive Gaussian confining potential'
Francisco M Fernández, Javier Garcia
We discuss a recently proposed analytical formula for the eigenvalues of the Gaussian well and compare it with the analytical expression provided by the variational method with the…
On the variational homotopy perturbation method for nonlinear oscillators
Francisco M. Fernández
In this paper we discuss a recent application of a variational homotopy perturbation method to rather simple nonlinear oscillators . We show that the main equations are inconsisten…
HAM and HPM: Another attack to reason
Francisco M. Fernández
We discuss two recent applications of homotopy analysis method and homotopy perturbation method and conclude that the results are completely useless from both mathematical and phys…
Nonsensical models for quantum dots
Francisco M. Fernández
We analyze a model proposed recently for the calculation of the energy of an exciton in a quantum dot and show that the authors made a serious mistake in the solution to the Schröd…
More integrals of products of Airy functions
Francisco M. Fernández
By means of a modified hypervirial theorem we derive simple expressions for the integrals of products of Airy functions. Present results contain earlier ones as particular cases.
On exact and perturbation solutions to nonlinear equations for heat transfer models
Francisco M. Fernández
We analyze some exact and approximate solutions to nonlinear equations for heat transfer models. We prove that recent results derived from a method based on Lie algebras are either…
Alternative Fourier-series approach to nonlinear oscillations
Francisco M. Fernández
We propose an alternative approach that avoids the nonlinear equations for the Fourier coefficients that appear in the method of harmonic balance. We apply it to two simple illustr…
On a simple approach to nonlinear oscillators
Francisco M. Fernández
We analyze a simple textbook approach to nonlinear oscillators proposed recently, disclose its errors, limitations and misconceptions and complete the calculations that the authors…
On the small--amplitude approximation to the differential equation
Francisco M. Fernández
We obtain the radius of convergence of the small--amplitude approximation to the period of the nonlinear oscillator with the initial conditions $x(0)=…
The virial theorem for nonlinear problems
Paolo Amore, Francisco M Fernández
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation p…
Comment on the numerical solutions of a new coupled MKdV system (2008 Phys. Scr. 78 045008)
Francisco M. Fernández
In this comment we point out some wrong statements in the paper by Inc and Cavlak, Phys. Scr. 78 (2008) 045008
Born-Oppenheimer approximation for a harmonic molecule
Francisco M. Fernández
We apply the Born--Oppenheimer approximation to a harmonic diatomic molecule with one electron. We compare the exact and approximate results not only for the internal degrees of fr…
New Approach to Bounded Quantum--Mechanical Models
Francisco M. Fernández
We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply…