We prove the existence of solutions to an integral equation modeling the infiltration of a fluid in an isotropic homogeneous porous medium. Let us consider the mathematical theory of the infiltration of a fluid from a cylindrical reservoir into an isotropic homogeneous porous medium. Describing this phenomena in the Boussinesq model (see [1]), we are led to the nonlinear integral equation (see ...

In this article, we give some results concerning the continuity of the nonlinear Volterra and Fredholm integral operators on the space L1[0,∞). Then by using the concept of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes of nonlinear integral equations. Our results extend some previous works.

Using the path-integral technique we examine the mutual information for the communication channel modelled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications — the backbone of the Internet. At large signal-to-...

Using the path-integral technique we examine the mutual information for the communication channel modeled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications-the backbone of the internet. At large signal-to-noi...

Most of the methods, which used to solve nonlinear integral equations, transform the equation into a system of nonlinear equations. It is cumbersome to solve these systems, or the solution may be unreliable. In this paper, we propose an iterative approach based on fixed point method and Sinc quadrature, which has exponentially rate of convergence, to solve Hammerstein integral equation. Converg...

where f, g : I × → are given functions, λ ∈ (0, 1]. The study of quadratic integral equation has received much attention over the last thirty years or so. For instance, Cahlon and Eskin [1] prove the existence of positive solutions in the space C[0, 1] and Cα[0, 1] of an integral equation of the Chandrasekhar H-equation with perturbation. Argyros [2] investigates a class of quadratic equations ...

The reduction of nonlinear ordinary differential equations by a combination of first integrals and Lie group symmetries is investigated. The retention, loss or even gain in symmetries in the integration of a nonlinear ordinary differential equation to a first integral are studied for several examples. The differential equations and first integrals are expressed in terms of the invariants of Lie...

Abstract: In this article, the approximate analytical solutions of the linear and nonlinear Abel type integral equation are obtained with the help of analytical method of linear and nonlinear problems called the Modified New Iterative Method (MNIM). By choosing initial value, the explicit solution of the integral equation for different examples have been solved which demonstrate the effectivene...