An Analysis on Different Algorithms and Methods of Schrodinger–Poisson–Slater Equation

Rajni  Rani; Dr. Yogesh  Kumar

An Analysis on Different Algorithms and Methods of Schrodinger–Poisson–Slater Equation

Investigating the Existence and Computation of Solitary Waves and Eigenpairs in a Schrodinger-Poisson System

by Rajni Rani*, Dr. Yogesh Kumar,

- Published in Journal of Advances in Science and Technology, E-ISSN: 2230-9659

Volume 10, Issue No. 20, Nov 2015, Pages 0 - 0 (0)

Published by: Ignited Minds Journals

ABSTRACT

We study the existence of radially symmetric solitarywaves for a non-linear Schrodinger-Poisson system. In contrast to all previousresults, we consider the presence of a positive potential, of interest inphysical applications. We present a new implementation of the two-grid methodfor computing extremum eigenpairs of self-adjoint partial differentialoperators with periodic boundary conditions. A novel two-grid centereddifference method is proposed for the numerical solutions of the nonlinearSchrödinger–Poisson (SP) eigenvalue problem. We solve the Poisson equation toobtain the nonlinear potential for the nonlinear Schrödinger eigenvalueproblem.

KEYWORD

Schrodinger-Poisson-Slater equation, radially symmetric solitary waves, positive potential, two-grid method, extremum eigenpairs, self-adjoint partial differential operators, periodic boundary conditions, centered difference method, nonlinear Schrödinger-Poisson eigenvalue problem, Poisson equation