http://repositorio.cualtos.udg.mx:8080/jspui/handle/123456789/1061 Tue, 07 Apr 2026 00:51:57 GMT 2026-04-07T00:51:57Z http://repositorio.cualtos.udg.mx:8080/jspui/handle/123456789/1674 Title: Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders Authors: Molina Holguín, Carlos Alberto; Urenda Cázares, Ernesto; Macías Díaz, Jorge E.; Gallegos, Armando Abstract: In this article, a generalized form of the Davey–Stewartson system, consisting of three nonlinear coupled partial differential equations, will be studied. The system considers the presence of fractional spatial partial derivatives of the Riesz type, and extensions of the classical mass, energy, and momentum operators will be proposed in the fractional-case scenario. In this work, we will prove rigorously that these functionals are conserved throughout time using some functional properties of the Riesz fractional operators. This study is intended to serve as a stepping stone for further exploration of the generalized Davey–Stewartson system and its wide-ranging applications. Mon, 01 Apr 2024 00:00:00 GMT http://repositorio.cualtos.udg.mx:8080/jspui/handle/123456789/1674 2024-04-01T00:00:00Z http://repositorio.cualtos.udg.mx:8080/jspui/handle/123456789/1566 Title: Integral of motion and nonlinear dynamics of three Duffing oscillators with weak or strong bidirectional coupling Authors: Urenda Cázares, Ernesto; Barba Franco, José de Jesús; Gallegos, Armando; Macías Díaz, Jorge E. Abstract: In this work, we present a system composed of three identical Duffing oscillators coupled bidirectionally. Starting from a Lagrangian that describes the system, an integral of motion is obtained by means of Noether’s theorem. The dynamics of the model is studied using bifurcation diagrams, Lyapunov exponents, time-series analysis, phase spaces, Poincaré sections, spatiotemporal and integral of motion planes. The analysis focuses on the monostable and bistable cases of the Duffing oscillator potential, in which a confined movement is guaranteed. In particular, it is observed that the system shows a chaotic behavior for small values of the coupling parameter for the bistable case. This is one of the first articles in the literature in which non-trivial integrals of motion are obtained for a system of three Duffing oscillators coupled bidirectionally. It is worth pointing out that there are some reports in the literature on integrals of motion for unidirectionally coupled nonlinear Duffing oscillators, but the study carried out in this work for bidirectionally coupled systems with more than two nonlinear Duffing oscillators is certainly one of the first. Description: Artículo Sun, 01 Oct 2023 00:00:00 GMT http://repositorio.cualtos.udg.mx:8080/jspui/handle/123456789/1566 2023-10-01T00:00:00Z http://repositorio.cualtos.udg.mx:8080/jspui/handle/123456789/1090 Title: Driven damped nth-power anharmonic oscillators with time-dependent coefficients and their integrals of motion Authors: Macías Díaz, Jorge Eduardo; Urenda Cázares, Ernesto; Gallegos Infante, Armando Abstract: In this manuscript, we derive integrals of motion for general anharmonic oscillators with damping and power-law forcing. The model under investigation has time-dependent coefficients, and the determination of these physical quantities is carried out using Noether´s theorem. The solutions must satisfy appropriate analytical conditions for the proposed quantities to be true integrals of motion. In turn, these analytical conditions are associated to well know physical systems, including the Milne-Pinney and Ermakov-Lewis models. We provide various numerical solutions of our equations of motion and the associated integrals to verify the theoretical results. Description: Artículo Tue, 01 Jun 2021 00:00:00 GMT http://repositorio.cualtos.udg.mx:8080/jspui/handle/123456789/1090 2021-06-01T00:00:00Z http://repositorio.cualtos.udg.mx:8080/jspui/handle/123456789/1070 Title: The noisy Pais–Uhlenbeck oscillator Authors: Urenda Cázares, Ernesto; Espinoza, Pedro Basilio; Gallegos Infante, Armando; Jaimes Reátegui, Rider; Macías Díaz, Jorge Eduardo; Vargas Rodríguez, Héctor Abstract: Abstract In this paper, we include simultaneously additive and multiplicative noise to the Pais–Uhlenbeck oscillator (PUO). We construct an integral of motion of the PUO with a time-dependent coefficient. Viewing the PUO as two coupled harmonic oscillators, we add noise to the corresponding frequencies. The systems are solved with the fourthorder stochastic Runge–Kutta method. Some graphics of the solutions and integrals of motion are presented, and the average deviations are calculated in order to quantify the noise influence. Resumen. En este artículo incluimos simultáneamente ruido aditivo y multiplicativo al oscilador Pais-Uhlenbeck (PUO). Construimos una integral de movimiento del PUO con un coeficiente dependiente del tiempo. Al considerar el PUO como dos osciladores armónicos acoplados, agregamos ruido a las frecuencias correspondientes. Los sistemas se resuelven con el método estocástico de Runge-Kutta de cuarto orden. Se presentan algunos gráficos de las soluciones e integrales de movimiento y se calculan las desviaciones medias para cuantificar la influencia del ruido. Wed, 01 May 2019 00:00:00 GMT http://repositorio.cualtos.udg.mx:8080/jspui/handle/123456789/1070 2019-05-01T00:00:00Z