A slightly modified variant of the cubic periodic one-dimensional nonlinear Schrödinger equation is shown to be well-posed, in a relatively weak sense, in certain function spaces wider than L. Solutions are constructed as sums of infinite series of multilinear operators applied to initial data, and these multilinear operators are analyzed directly.

harmonics have become an important issue in modern power systems. the widespread penetration of non-linear loads to emerging power systems has turned power quality analysis into an important operation issue under both steady state and transient conditions. this paper employs an extended harmonic domain (ehd) based framework for dynamic analysis of long term analysis over voltages during the tra...

In this paper, the general solution of steady-state two-dimensional non-axisymmetric mechanical and thermal stresses and mechanical displacements of a hollow thick cylinder made of fluid-saturated functionally graded porous material (FGPM) is presented. The general form of thermal and mechanical boundary conditions is considered on the inside and outside surfaces. A direct method is used to sol...

In this paper, a new identification of the Lagrange multipliers by means of the Sumudu transform, is employed to  btain a quick and accurate solution to the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Undoubtedly this model is the most well known model for pricing financial derivatives. The fractional derivatives is described in Caputo sen...

in this paper, the homotopy analysis method (ham) is considered to obtain the solution of the schrodinger equation with a power law nonlinearity. for this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. also, an example is solved to illustrate the eciency of the mentioned algorithm and the h-curve is plotted to determine the region...

This article investigates different nonlinear systems of fractional partial differential equations analytically using an attractive modified method known as the Laplace residual power series technique. Based on a combination transformation and technique, we achieve analytic approximation results in rapid convergent form by employing notion limit, with less time effort than method. Three challen...