Using analytical and numerical techniques we analyze the static and dynamical properties of solitonlike excitations in the presence of parametric disorder in the one-dimensional nonlinear Schrödinger equation with a homogeneous power nonlinearity. Both the continuum and the discrete problem are investigated. We find that otherwise unstable excitations can be stabilized by the presence of disorder in the continuum problem. For the very narrow excitations of the discrete problem we find that the disorder has no effect on the averaged behavior. Finally, we show that the disorder can be applied to induce a high degree of controllability of the spatial extent of the stable excitations in the continuum system. ͓S0163-1829͑97͒06346-7͔
We present a partial panoramic view of possible contexts and applications of the fractional calculus. In this context, we show some different applications of fractional calculus to different models in ordinary differential equation (ODE) and partial differential equation (PDE) formulations ranging from the basic equations of mechanics to diffusion and Dirac equations.
Abstract:An approach to model the Martian magnetization can be done using classical source models. Classical models, such as uniformly magnetized spheres and cylinders, allow for the introduction of additional constraints related to the available information of the magnetic field and its sources. The use of a suitable conservative numerical scheme in Cartesian coordinates was carried out for numerical studies. In this work the motion of different charged particles under the influence of different magnetized sources have been analyzed by using the proposed numerical scheme. For that purpose, electron, proton and alpha particles were used. In addition, the impact of the gravitational effect on the particles motion was also studied.PACS (2008)
The dust aerosols floating in the atmosphere of Mars cause an attenuation of the solar radiation traversing the atmosphere that cannot be modeled through the use of classical diffusion processes. However, the definition of a type of fractional diffusion equation offers a more accurate model for this dynamic and the second order moment of this equation allows one to establish a connection between the fractional equation and the Ångstrom law that models the attenuation of the solar radiation. In this work we consider both one and three dimensional wavelength-fractional diffusion equations, and we obtain the analytical solutions and numerical methods using two different approaches of the fractional derivative.
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