arXiv subjects

Pedro Franco

Publications and source records attributed to Pedro Franco.

2 recordsLinked to original sources

arXiv2018

Solution of the Nonlinear Schrodinger Equation with Defocusing Strength Nonlinearities Through the Laplace-Adomian Decomposition Method

In this work we apply the Adomian decomposition method combined with the Laplace transform (LADM) in order to solve the 1-dimensional nonlinear Schrodinger equation whose nonlinear term presents a nonlinear defocusing strength that varies in the spatial direction. The suggested iterative scheme (LADM) finds the solution without any discretization, linearization or restrictive assumptions. Finally, three numerical examples are presented to demonstrate the reliability and accuracy of the method.

physics.comp-ph↗

arXiv2012

On Fourier integral transforms for $q$-Fibonacci and $q$-Lucas polynomials

We study in detail two families of $q$-Fibonacci polynomials and $q$-Lucas polynomials, which are defined by non-conventional three-term recurrences. They were recently introduced by Cigler and have been then employed by Cigler and Zeng to construct novel $q$-extensions of classical Hermite polynomials. We show that both of these $q$-polynomial families exhibit simple transformation properties with respect to the classical Fourier integral transform.

math-ph↗