436 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Consejo Nacional de Investigaciones Científicas y TécnicasAR144 papers
- Universidad Nacional de La PlataAR72 papers
- Universidad de ColimaMX41 papers
- Centro Científico Tecnológico - La PlataAR40 papers
- Institute for Complex SystemsIT23 papers
- Sapienza University of RomeIT22 papers
- University of TrentoIT18 papers
- Centre National de la Recherche ScientifiqueFR13 papers
- Instituto de Fisica de Liquidos y Sistemas BiologicosAR13 papers
- University of MichiganUS12 papers
- Cornell UniversityUS11 papers
- University of CambridgeGB11 papers
28 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…
Weakly bound states in heterogeneous waveguides
Paolo Amore, Francisco M. Fernandez, Christoph P. Hofmann
We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet bound…
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…
Rayleigh-Ritz variational method with suitable asymptotic behaviour
Javier Garcia, Francisco M Fernández
We discuss Rayleigh-Ritz variational calculations with nonorthogonal basis sets that exhibit the correct asymptotic behaviour. We construct the suitable basis sets for general one-…
-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…
Critical parameters for non-hermitian Hamiltonians
Francisco M Fernández, Javier Garcia
We calculate accurate critical parameters for a class of non-hermitian Hamiltonians by means of the diagonalization method. We study three one-dimensional models and two perturbed…
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…
Accurate calculation of the eigenvalues of a new simple class of superpotentials in SUSY quantum mechanics
Francisco M. Fernández
We obtain accurate eigenvalues for two recently derived SUSY partner Hamiltonians. We improve the Rayleigh-Ritz variational method proposed by the authors and show how to apply 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…
Accurate calculation of resonances for a central-field model potential
Francisco M. Fernández
We obtain accurate resonance energies for the Schrödinger equation with a central--field potential by means of a method based on a rational approximation to the logarithmic derivat…
On a perturbation treatment of a model for MHD viscous flow
Francisco M. Fernández
We discuss the solution of a nonlinear ordinary differential equation that appears in a model for MHD viscous flow caused by a shrinking sheet. We propose an accurate numerical sol…
On the homotopy perturbation method for Boussinesq-like equations
Francisco M. Fernández
We comment on some analytical solutions to a class of Boussinesq-like equations derived recently by means of the homotopy perturbation method (HPM). We show that one may obtain exa…
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…
On some approximate methods for nonlinear models
Francisco M. Fernández
We show that recent applications of the homotopy perturbation method the Adomian decomposition method and the variational iteration method are completely useless for the treatment…
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
Eigenvalues from power--series expansions: an alternative approach
P. Amore, F. M. Fernandez
An appropriate rational approximation to the eigenfunction of the Schrödinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a…
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…
On nonadiabatic calculation of dipole moments
Francisco M. Fernandez
We show that a recent non Born--Oppenheimer calculation of dipole moments exhibits obscure points and is not consistent with the well known Hellmann--Feynman theorem.
Rayleigh-Ritz variation method and connected-moments polynomial approach
Francisco M. Fernandez
We show that the connected-moments polynomial approach proposed recently is equivalent to the well known Rayleigh-Ritz variation method in the Krylov space. We compare the latter w…
Accurate eigenvalues of bounded oscillators
Francisco M. Fernandez
We calculate accurate eigenvalues of a bounded oscillator by means of the Riccati--Padé method that is based on a rational approximation to a regularized logarithmic derivative of…
Accurate calculation of the complex eigenvalues of the Schrödinger equation with an exponential potential
Paolo Amore, Francisco M. Fernandez
We show that the Riccati--Padé method is suitable for the calculation of the complex eigenvalues of the Schrödinger equation with a repulsive exponential potential. The accuracy of…
Calculation of bound states and resonances in perturbed Coulomb models
Francisco M. Fernandez
We calculate accurate bound states and resonances of two interesting perturbed Coulomb models by means of the Riccati-Padé method. This approach is based on a rational approximatio…
Accurate calculation of resonances in multiple-well oscillators
Francisco M. Fernandez
Quantum--mechanical multiple--well oscillators exhibit curious complex eigenvalues that resemble resonances in models with continuum spectra. We discuss a method for the accurate c…
Inversion of perturbation series
Paolo Amore, Francisco M. Fernandez
We investigate the inversion of perturbation series and its resummation, and prove that it is related to a recently developed parametric perturbation theory. Results for some illus…