The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to non integrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the 2D Ginzburg-Landau equation.

In this paper we investigate the existence and uniqueness for Volterra-Fredholm type integral equations and extension of this type of integral equations. The result is obtained by using the  coupled fixed point theorems in the framework of Banach space $ X=C([a,b],mathbb{R})$. Finally, we  give an example to illustrate the applications of our results.

This article proposes an optimal method for approximate answer of stochastic Ito-Voltrra integral equations, via rationalized Haar functions and their stochastic operational matrix of integration. Stochastic Ito-voltreea integral equation is reduced to a system of linear equations. This scheme is applied for some examples. The results show the efficiency and accuracy of the method.

A crucial ingredient in the formulation of boundary-value problems for acoustic scattering of time-harmonic waves is the radiation condition. This is well understood when the scatterer is a bounded obstacle. For plane-wave scattering by an infinite, rough, impenetrable surface S , the physics of the problem suggests that all scattered waves must travel away from ~or along! the surface. This con...

A quasi Riemann surface is defined to be a certain kind of complete metric space Q whose integral currents are analogous to the integral currents of a Riemann surface. In particular, they have properties sufficient to express Cauchy-Riemann equations on Q. The prototypes are the spaces D 0 (Σ)m of integral 0-currents of total mass m in a Riemann surface Σ (usually called the integral 0-cycles o...

How to get the original ideas” is the fundamental and critical issue for the researchers in science and technology. In this paper, the author writes his experiences concerning how he could encounter the interesting and original ideas of three research subjects, i.e., the accelerating medium effect, the guided-mode extracted integral equation and the surface plasmon gap waveguide. key words: ide...

the principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (iae) by using the bernoulli polynomials and the residual correction method. after implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown bernoulli coefficients. thismethod gives an analytic solution when t...

in this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. but we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as legendre ...