Generalized Jacobi Elliptic Function Method for Traveling Wave Solutions of Some Nonlinear Schrödinger’s Equations

Abstract

In this study, we found the traveling wave solutions of these equations by applying (3+1)-dimensional nonlinear Schrödinger’s equation and coupled nonlinear Schrödinger’s equation to Generalized Jacobi elliptic function method. We have expressed these solutions both as Jacobi elliptical solutions and trigonometric and hyperbolic solutions. We present two and three dimensional graphics of some solutions we have found. We also state some studies on these equations.

Keywords

• Generalized Jacobi elliptic function method,(3+1)-dimensional nonlinear Schrödinger’s equation,coupled nonlinear Schrödinger’s equation,traveling wave solutions

Bazı Doğrusal Olmayan Schrödinger Denklemlerinin Hareketli Dalga Çözümleri İçin Genelleştirilmiş Jacobi Eliptik Fonksiyon Yöntemi

Öz

Bu çalışmada (3 + 1) boyutlu doğrusal olmayan Schrödinger denklemine ve doğrusal olmayan Schrödinger denklem çiftine Genelleştirilmiş Jacobi eliptik fonksiyon yöntemini uygulayarak bu denklemlerin hareketli dalga çözümlerini bulduk. Bu çözümleri hem Jacobi eliptik çözümler hem de trigonometrik ve hiperbolik çözümler olarak ifade ettik. Bulduğumuz bazı çözümlerin iki ve üç boyutlu grafiklerini sunduk. Ayrıca bu denklemler üzerine yapılan bazı çalışmaları ifade ettik.

Anahtar Kelimeler

• Genelleştirilmiş Jacobi eliptik fonksiyon yöntemi,(3 + 1) boyutlu doğrusal olmayan Schrödinger denklemi,doğrusal olmayan Schrödinger denklem çifti,hareketli dalga çözümleri

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