In this paper we study a quasilinear elliptic system coupled by Schrödinger equation with p-Laplacian operator and Poisson equation. Some scaling transformation ingenious methods are applied to produce the bounded Palais-Smale sequences existence of nontrivial solutions for is obtained mountain pass theorem.

In this paper, we investigate the time M-fractional modified nonlinear Schrödinger equation that describes propagation of rogue waves in deep water. Periodic, solitary, and kink (or anti-kink) wave solutions are discussed using bifurcation theory for planar integrable systems. Some new constructed first integral traveling system. The degeneracy obtained is investigated by transition between orb...

Fractional partial differential equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we propose a local discontinuous Galerkin (LDG) method for the distributedorder time and Riesz space fractional convection-diffusion and Schrödinger type equations. We prove stability and optimal order of convergence O(h + (∆t) θ 2 + θ) for the distr...

This paper considers random balls in a D-dimensional Euclidean space whose centers are prescribed by a homogeneous Poisson point process and whose radii are prescribed by a specific power law. A random field is constructed by counting the number of covering balls at each point. Even though it is not Gaussian, this field shares the same covariance function as the fractional Brownian field (fBf)....

Using inverse subordinators and Mittag-Leffler functions, we present a new definition of a fractional Poisson process parametrized by points of the Euclidean space R+. Some properties are given and, in particular, we prove a long-range dependence property.

We present a parallel solution of the Schrr odinger{Poisson system on distributed memory machines. The Schrr odinger{Poisson system is an evolution model for the numerical simulation of a collisionless electron plasma. We apply the Galerkin{Fourier method to the one{ dimensional system which results in a nonlinear system of ordinary differential equations. This initial value problem is solved b...

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...