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Articles
Published: 2022-12-22

The Generalized Petviashvili Iteration Method for Determined Stationary Waves Solutions of Nonlinear Schrödinger Equations with Potential Function V(x)

Prodi Matematika FMIPA Universitas Mataram
UIN Mataram
a generalized Petviashvili iteration method; stationary wave; Nonlinear Schrödinger equation; Bose-Einstein condensation; potential function

Abstract

This research discusses a numerical method for determining the stationary waves as a solution of Nonlinear Schrödinger (NLS) equations. In general, solutions for the partial differential equations can be solved analytically. However, most the solutions of the nonlinear wave equations are difficult to determine analytically. Therefore, a numerical approach is needed to determine the solution of the NLS equation. One of the numerical methods can be used to find the solution of the NLS equation is the Petviashvili iteration method. For case study, the NLS equation has been generated by the theory of Bose-Einstein condensation which contain potential function . To solve this problem, we generalized Petviashvili iteration method to determine the stationary waves solution easily. The most interesting result for this study is by modification of Petviashvili iteration method, we can make it easier to find a stationary solution for the nonlinear Schrodinger equation which containing the Bose-Einstein condensation potential function .

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