We investigate the nonlocal behavior of passive tracer dispersion with random stopping at various sites in fluids. This kind of dispersion processes is modeled by an integral partial differential equation, i.e., an advection-diffusion equation with a memory term. We have shown the exponential decay of the passive tracer concentration, under suitable conditions for the velocity field and the pro...

In this article we study the generalized dispersion version of the Kadomtsev-Petviashvili II equation, on T × R and T × R. We start by proving bilinear Strichartz type estimates, dependent only on the dimension of the domain but not on the dispersion. Their analogues in terms of Bourgain spaces are then used as the main tool for the proof of bilinear estimates of the nonlinear terms of the equa...

An optimized explicit modified Runge-Kutta RK method for the numerical integration of the radial Schrödinger equation is presented in this paper. This method has frequency-depending coefficients with vanishing dispersion, dissipation, and the first derivative of dispersion. Stability and phase analysis of the new method are examined. The numerical results in the integration of the radial Schröd...

We show that any L solution of the Gabitov-Turitsyn equation describing dispersion managed solitons decay exponentially in space and frequency domains. This confirms in the affirmative Lushnikov’s conjecture of exponential decay of dispersion managed solitons.

We study propagation of dispersion-managed solitons in optical fibers which are modeled by the nonlinear Schrödinger equation with a periodic dispersion coefficient. When the dispersion variations are weak compared to the average dispersion, we develop perturbation series expansions and construct asymptotic solutions at the first and second orders of approximation. Due to a parametric resonance...

We analyze self-focusing and singularity formation in the nonlinear Schrödinger equation (NLS) with high-order dispersion iψt±∆ψ+ |ψ|2σψ = 0, in the isotropic mixed-dispersion NLS iψt + ∆ψ + ǫ∆2ψ + |ψ|2σψ = 0, and in nonisotropic mixed-dispersion NLS equations which model propagation in fiber arrays.

One dimensional propagation of ultraslow optical pulses in an atomic BoseEinstein condensate taking into account the dispersion and the spatial inhomogeneity is investigated. Analytical and semi-analytical solutions of the dispersive inhomogeneous wave equation modeling the ultraslow pulse propagation are developed and compared against the standard wave equation solvers based upon Cranck-Nichol...

In this paper, we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE). The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order β ∈ (1,2]. We propose an implicit finite difference approximation for RSFRDE. The stability and convergence of the finite difference approximations are ana...

In the present paper Haar wavelet method is implemented on advectiondispersion equation representing one dimensional contaminant transport through a porous medium. Non uniform flow is considered by assuming velocity and dispersion varying with time as an exponentially increasing function. Expressing the Haar wavelets in advection-dispersion equation into Haar series provides the main advantage ...

Narrow optical dip solutions are investigated when, besides self-phase modulation and group velocity dispersion, also third-order dispersion, nonlinear dispersion, and stimulated Raman scattering are taken into account. By using the inverse scattering transform for the higher-order optical nonlinear Schrödinger (HNLS) equation under Hirota parameter conditions, the dark N-soliton solution is co...