Lineer Olmayan bir Schrödinger Denkleminin Galerkin Metoduyla Çözümü

Bu çalışmada iki boyutlu lineer olmayan bir Schrödinger denklemi için bir başlangıç sınır değer problemigöz önüne alırız. Galerkin metodunu kullanarak başlangıç sınır değer probleminin çözümünün var ve tek olduğunuispatlarız. Ayrıca, başlangıç sınır değer probleminin çözümü için bir değerlendirme elde ederiz.

Anahtar Kelimeler:

Başlangıç sınır değer problemi, Galerkin metodu, Schrödinger denklemi

Solution of a Nonlinear Schrödinger Equation with Galerkin’s Method

In this paper, we consider an initial boundary value problem for a two-dimensional nonlinearSchrödinger equation. We prove by using Galerkin’s method that the solution of the initial boundary value problemexists and it has a unique solution. Also, we get an estimation for the solution of the initial boundary value problem.

Keywords:

Galerkin method, initial boundary value problem, Schrödinger equation,

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