In this paper we present two new methods based on an implicit Runge-Kutta method Gauss which is of algebraic order fourth and has two stages: the first one has zero dispersion and the second one has zero dispersion and zero dissipation. The efficiency of these methods is measured while integrating the radial Schrödinger equation and other well known initial value problems.

We have employed our recently developed Green’s function formalism to study the dielectric behavior of a model membrane, formed by two periodic interfaces separating two media of different dielectric constants. The Maxwell’s equations are converted into a surface integral equation; thus it greatly simplifies the solutions and yields accurate results for membranes of arbitrary shape. The integra...

Stationary structures in a classical isotropic two-dimensional continuous Heisenberg ferromagnetic spin system are studied in the framework of the (2 + 1)-dimensional Landau–Lifshitz model. It is established that in the case of ~ S(~r, t) = ~ S(~r − ~vt) the Landau–Lifshitz equation is closely related to the Ablowitz–Ladik hierarchy. This relation is used to obtain soliton structures, which are...

A unified analytical description of the evolution of quasi-linear optical pulses and solitons in strongly dispersion-managed transmission systems is developed. Asymptotic analysis of the nonlocal equation that describes the averaged dynamics of a dispersion-managed system shows that the nonlinearity decreases for large map strength s , as O(log s/s) . The spectral intensity is found to be an in...

Wave packet broadening in usual quantum mechanics is a consequence of dispersion behavior of the medium which the wave propagates in it. In this paper, we consider the problem of wave packet broadening in the framework of Generalized Uncertainty Principle(GUP) of quantum gravity. New dispersion relations are derived in the context of GUP and it has been shown that there exists a gravitational i...

We study the decay and smoothness of solutions of the dispersion managed non-linear Schrödinger equation in the case of zero residual dispersion. Using new x-space versions of bilinear Strichartz estimates, we show that the solutions are not only smooth, but also fast decaying.

Mixing-transport of solute entering at sinkholes or from within the limestone matrix in cavernous conduits is an important process for contaminant migration in karst aquifers. This process may be described with a one-dimensional advection-dispersion equation incorporating the fluxes of solute and water across the conduit wall. For the dilution-dispersion equation, which does not include solute ...

The finite-difference-time-domain (FDTD), although recognized as a flexible, robust and simple to implement method for solving complex electromagnetic problems, is subject to numerical dispersion errors. In addition to the traditional ways for reducing dispersion, i.e., increasing sampling rate and using higher order degrees of accuracy, a number of schemes have been proposed recently. In this ...

For time-domain modeling based on the acoustic wave equation, spectral methods have recently demonstrated promise. This letter presents an extension of a spectral domain decomposition approach, previously used to solve the lossless linear wave equation, which accommodates frequency-dependent atmospheric attenuation and assignment of arbitrary dispersion relations. Frequency-dependence is straig...

Using an asymptotic analysis, we obtain an eigenvalue equation for the general mode dispersion in Bragg fibers. The asymptotic analysis is applied to calculate the dispersion relation and the field distribution of TE modes in a Bragg fiber. We compare the asymptotic results with exact solutions and find excellent agreement between them. This asymptotic approach greatly simplifies the analysis a...