The staggered-grid finite-difference (FD) method is widely used in numerical simulation of the wave equation. With stability conditions, grid dispersion often exists because of the discretization of the time and the spatial derivatives in thewave equation. Therefore, suppressing grid dispersion is a key problem for the staggered-grid FD schemes. To reduce the grid dispersion, the traditional me...

Chaotic mode-locking of chirped-pulse oscillator has been analyzed on the basis of generalized nonlinear cubic-quintic complex Ginzburg-Landau equation. It has been shown, that the chirped solitary pulse can be stabilized against the vacuum excitation, if the fourth-order dispersion is nonzero and positive. However, the pulse evolves chaotically, if the dispersion reaches some threshold value.

Recently, an exact Eulerian-Lagrangian theory of advective transport in spacetime random velocity fields was developed by one of us. We present a formal extension of this theory that accounts for anisotropic local dispersion. The resultant (conditional) mean transport equation is generally nonlocal in space-time. To assess the impact of local dispersion on the prediction of transport under unce...

The Hirota equation is a higher order extension of the nonlinear Schrödinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete per...

In the last three decades, interest in fractional calculus has experienced rapid growth and at present we can find many papers devoted its theoretical and application aspects (see the work of Machado et al. (2011) and the references therein). Fractional order models of real systems are often more adequate than the usually used integer order models in electrochemistry (Ichise et al., 1971), adve...

The differential migration of ions in an applied electric field is the basis for separation of chemical species by capillary electrophoresis. Axial diffusion of the concentration peak limits the separation efficiency. Electromigration dispersion is observed when the concentration of sample ions is comparable to that of the background ions. Under such conditions, the local electrical conductivit...

A temporal stability analysis was carried out to model the atomization of a swirling viscous non-Newtonian annular liquid sheet emanating from an air-blast atomizer subject to inner and outer inviscid swirling air streams. The dimensionless dispersion equation that governs the instability of a viscous non-Newtonian annular liquid sheet under swirling air streams was obtained. Numerical solution...

The numerical simulation of a level IV fugacity model coupled to a dispersion-advection equation to simulate the environmental concentration of a pesticide in rice fields is presented. The model simulates the dynamic distribution of the pesticide in a compartmental system constituted by air, water, rice plants and bottom sediment together with saturated soil layers. The level IV fugacity model ...

Numerical solutions of the Helmholtz equation suffer from numerical pollution especially for the case of high wavenumbers. The major component of the numerical pollution is, as has been reported in the literature, the dispersion error which is defined as the phase difference between the numerical and the exact wave. The dispersion error for the meshless methods can be a priori determined at an ...

The complex dispersion characteristics of the surface wave modes of plasma column loaded closed cylindrical waveguides have been investigated. The numerical results for partially or fully plasma loaded waveguides have been obtained from the Method of Moment (MOM), the exact dispersion equation and the quasistatic dispersion equation. A numerical technique based on the solution of the MoM has be...