New Exact Solutions of Cubic Nonlinear Schrödinger Equation by Using Extended Trial Equation Method

Year 2020, Volume: 20 Issue: 4, 582 - 588, 25.09.2020

Yusuf Pandır , Tural Ağır

https://doi.org/10.35414/akufemubid.709937

Cited By: 2

Abstract

In this study, the extended trial equation method, which allows to obtain exact solutions of the partial differential equations, is investigated. This proposed method is applied to the cubic nonlinear Schrödinger equation and different new exact solutions are obtained. We can state that these new exact solutions are new exact solutions that are not find in the literature. In addition, two and three dimensional graphics drawn to show the physical behavior of these new exact solutions. 

In this study, the extended trial equation method, which allows to obtain exact solutions of the partial differential equations, is investigated. This proposed method is applied to the cubic nonlinear Schrödinger equation and different new exact solutions are obtained. We can state that these new exact solutions are new exact solutions that are not find in the literature. In addition, two and three dimensional graphics drawn to show the physical behavior of these new exact solutions. 

Keywords

Extended Trial Equation Method, Nonlinear Partial Differential Equations, Schrödinger Equation with a Cubic Nonlinearity, Exact Solutions

Genişletilmiş Deneme Denklemi Yöntemi ile Kübik Lineer Olmayan Schrödinger Denkleminin Yeni Tam Çözümleri

Abstract

Bu çalışmada, kısmi türevli diferansiyel denklemlerin tam çözümlerinin elde edilmesine olanak sağlayan genişletilmiş deneme denklem yöntemi incelenmiştir. Önerilen bu yöntem kübik lineer olmayan Schrödinger denklemine uygulanmış ve farklı yeni tam çözümleri elde edilmiştir. Elde edilen bu yeni tam çözümlerin literatürde bulunmayan yeni tam çözümleri olduğunu ifade edebiliriz. Ayrıca, bulunan bu yeni tam çözümlerin fiziksel davranışlarını göstermek için iki ve üç boyutlu grafikleri çizilmiştir.

Bu çalışmada, kısmi türevli diferansiyel denklemlerin tam çözümlerinin elde edilmesine olanak sağlayan genişletilmiş deneme denklem yöntemi incelenmiştir. Önerilen bu yöntem kübik lineer olmayan Schrödinger denklemine uygulanmış ve farklı yeni tam çözümleri elde edilmiştir. Elde edilen bu yeni tam çözümlerin literatürde bulunmayan yeni tam çözümleri olduğunu ifade edebiliriz. Ayrıca, bulunan bu yeni tam çözümlerin fiziksel davranışlarını göstermek için iki ve üç boyutlu grafikleri çizilmiştir.

Keywords

Genişletilmiş Deneme Denklem Yöntemi, Kısmi Türevli Diferansiyel Denklemler, Kübik Lineer Olmayan Schrödinger Denklemi, Tam Çözümler

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