Öz faz modülasyonunun Kerr Yasası formuna sahip yüksek mertebeden doğrusal olmayan Schrödinger denkleminin optik soliton çözümleri

Abstract

Bu makalenin temel amacı, fiber optiklerde dispersif darbelerin yayılımını tanımlayan, kendi kendine faz modülasyonu ve Kerr yasası doğrusal olmayanlığı ile karakterize edilen yüksek mertebeden doğrusal olmayan Schrödinger denklemini incelemek ve birleşik Riccati denklemi genişletme yöntemini kullanmaktır. Amacımız yalnızca makalede önerilen teknikle çeşitli soliton çözümleri elde etmekle sınırlı değildir; aynı zamanda incelenen modelde yüksek mertebeden dispersiyon terimlerinin soliton yayılımı üzerindeki etkisini araştırmaktır. Yüksek mertebeden dispersiyon terimleri ve Kerr yasası ortamının etkisiyle incelenen modele ait yeni ve önemli fiziksel özellikler literatüre kazandırılmıştır. Ayrıca, model parametrelerinin uygun değerleri için bazı soliton çözümlerinin dinamik davranışları ve fiziksel önemi gösterilmiştir. Elde edilen soliton çözümleri arasında karanlık ve M-şekilli solitonlar bulunmaktadır. Bu çözümlerin fiziksel önemini yorumlamak amacıyla 3D, 2D ve kontur grafikleri sunulmuştur. Önerilen yaklaşımın, çeşitli karmaşık doğrusal olmayan problemlere optik çözümler elde etmek için etkili bir analitik yöntem olduğu gözlemlenmiştir.

Keywords

• Fiber optik
• Parametre etkisi
• Yüksek mertebeden dağılım
• M-şekilli soliton

Optical soliton solutions of the higher-order nonlinear Schrödinger equation with Kerr law nonlinearity of self-phase modulation

Abstract

The primary aim of this article is to examine the higher-order nonlinear Schrödinger equation, which describes the propagation of dispersive pulses in fiber optics, characterized by self-phase modulation and Kerr law nonlinearity, and to employ the unified Riccati equation expansion method. Our objective is not only limited to obtaining various soliton solutions using the technique proposed in the article but also to investigate the impact of higher-order dispersion terms on soliton propagation in the examined model. New and significant physical features of the investigated model, influenced by higher-order dispersion terms and Kerr law media, have been added to the literature. Furthermore, the dynamic behaviors and physical significance of some soliton solutions for appropriate values of the model parameters have been demonstrated. The obtained soliton solutions include dark and M-shaped solitons. The 3D, 2D, and contour plots of these solutions are presented to interpret the physical significance of the problem under consideration. It has been observed that the proposed approach is an effective analytical method that can be utilized to obtain optical solutions to various complex nonlinear problems.

Keywords

• Optical fibers
• Parameter effect
• High order dispersion
• M-shape soliton

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