Using a generalized transfer matrix method we exactly solve the Schrödinger equation in a time periodic potential, with discretized Euclidean space-time. The ground state wave function propagates in space and time with an oscillating soliton-like wave packet and the wave front is wedge shaped. In a statistical mechanics framework our solution represents the partition sum of a directed polymer s...

In this paper, we investigate periodic solutions of linear and nonlinear discrete Volterra equations of convolution or non-convolution type with unbounded memory. For linear discrete Volterra equations of convolution type, we establish Fredholm’s alternative theorem and for equations of non-convolution type, and we prove that a unique periodic solution exists for a particular bounded initial fu...

A numerically reliable state space algorithm is proposed for computing normalized coprime factorizations of periodic descriptor systems. A preprocessing step is used in the algorithm to convert the initial problem for possibly non-causal systems into a simpler problem for causal periodic systems. The main computational ingredient here is the computation of a coprime factorization with causal fa...

in this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. the homotopy analysis method (ham) is used for solving this equation. several examples are given to reconfirm the efficiency of these algorithms. the results of applying this procedure...

Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic ...

A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the one-dimensional complex Ginzburg-Landau equation (CGLE) with periodic boundary conditions. A relative periodic solution is a solution that is periodic in time, up to a transformation by an element of the equ...

In this paper, He’s amplitude frequency formulation is used to obtain a periodic solution for a nonlinear oscillator with fractional potential. By calculation and computer simulations, compared with the exact solution shows that the result obtained is of high accuracy. Keywords—He’s amplitude frequency formulation; Periodic solution; Nonlinear oscillator; Fractional potential.

We unify the concepts of G-metric, metric-like, and b-metric to define new notion of generalized b-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes of G-α -admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, so...

In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations), two main approaches are presented. The first is via Poincaré’s translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links wit...

The present study has used soil samples from Nigeria, contaminated with Brass crude-oil, to determine its biodegradation through enhanced biostimulation with cow dung and periodic aeration. Over a period of twenty-eight days, the hydrocarbon-utilizing bacteria (HUB) and hydrocarbon-utilizing fungi (HUF) have been counted and identified. Results from biodegradation of the brass crude-oil over th...