Examinando por Autor "Puertas-Centeno, David"

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A new pair of transformations and applications to generalized informational inequalities and Hausdorff moment problem
(Elsevier, 2025-12) Iagar, Razvan Gabriel; Puertas-Centeno, David
classes of probability densities in R. These transformations have the property of interchanging the main informational measures such as 𝑝−moments, Shannon and Rényi entropies, and Fisher information. We thus apply them in order to establish extensions and generalizations of the Stam and moment-entropy inequalities in a mirrored domain of the entropic indexes. Moreover, with the aid of the two transformations we establish formal solutions to the Hausdorff entropic moment problem by connecting them with the solutions of the standard Hausdorff problem. In addition, we introduce a Fisher-like moment problem and relate it to the standard Hausdorff moment problem.
Generalized and new solutions of the NRT nonlinear Schrödinger equation
(Elsevier, 2024-12-30) Gordoa, Pilar R.; Pickering, Andrew; Puertas-Centeno, David; Toranzo, E. V.
In this paper we present new solutions of the non-linear Schrödinger equation proposed by Nobre, Rego-Monteiro and Tsallis for the free particle, obtained from different Lie symmetry reductions. Analytical expressions for the wave function, the auxiliary field and the probability density are derived using a variety of approaches. Solutions involving elliptic functions, Bessel and modified Bessel functions, as well as the inverse error function are found, amongst others. On the other hand, a closed-form expression for the general solution of the traveling wave ansatz (see Bountis and Nobre) is obtained for any real value of the nonlinearity index. This is achieved through the use of the so-called generalized trigonometric functions as defined by Lindqvist and Drábek, the utility of which in analyzing the equation under study is highlighted throughout the paper.