Soliton Solutions of the Generalized Dullin-Gottwald-Holm Equation with Parabolic Law Nonlinearity

Yıl 2023, Sayı: 50, 171 - 177, 30.04.2023

Melih Çınar

https://doi.org/10.31590/ejosat.1270371

Öz

In this paper, soliton solutions of the generalized Dullin-Gottwald-Holm (gDGH) equation with parabolic law nonlinearity are investigated. The gDGH describes the behavior of waves in shallow water with surface tension. There are only a few studies in the literature regarding gDGH equation with parabolic law nonlinearity, and to our best knowledge, the unified Riccati equation expansion method (UREEM) has not been applied to this equation before. Many soliton solutions of the considered gDGH equation are successfully attained using the UREEM, which is a powerful technique for solving nonlinear partial differential equations. We verify that the obtained analytical solutions satisfy the gDGH equation using Mathematica. Furthermore, some plots of the acquired solitons are demonstrated with the aid of Matlab to examine the properties of the soliton solutions. The obtained results show that the considered gDGH equation admits dark, bright, singular, and periodic solutions. This study may contribute to a comprehensive investigation of the soliton solutions of the gDGH equation, which has practical applications in fields such as oceanography and nonlinear optics.

Anahtar Kelimeler

Soliton solutions, shallow water, nonlinear wave dynamics, dark soliton.

Parabolik Doğrusal olmayan Kanunlu Genelleştirilmiş Dullin-Gottwald-Holm Denkleminin Soliton Çözümleri

Öz

Bu makalede, parabolik yasalı genelleştirilmiş Dullin-Gottwald-Holm (gDGH) denkleminin soliton çözümleri incelenmiştir. İlgili denklem yüzey gerilimli sığ sularda dalga davranışını modellemektedir. Literatürde doğrusal olmayan parabolik kanuna sahip gDGH denklemi ile ilgili sadece birkaç çalışma vardır ve literatür araştırmalarından görüldüğü üzere bu makalede kullanılacak olan birleştirilmiş Riccati denklemi genişletme (BRDG) yöntemi daha önce bu denkleme uygulanmamıştır. Bu çalışmada gDGH denkleminin birçok soliton çözümü, doğrusal olmayan kısmi diferansiyel denklemleri çözmek için güçlü bir teknik olan BRDG yöntemi kullanılarak başarılı bir şekilde elde edilmiştir. Elde edilen analitik çözümlerin gDGH denklemini sağladığı Mathematica kullanarak doğrulanmıştır. Ayrıca, soliton çözümlerinin özelliklerini ve davranışını incelemek için elde edilen solitonların bazı grafikleri Matlab yardımıyla çizdirilmiştir. Elde edilen sonuçlar, gDGH denkleminin karanlık, parlak, tekil ve periyodik gibi farklı türlerde çözümler içerdiğini göstermektedir. Bu çalışma, okyanus bilimi ve doğrusal olmayan optik gibi alanlarda uygulamaları olan gDGH denkleminin soliton çözümlerinin kapsamlı bir şekilde incelenmesine katkı sunabilir.

Anahtar Kelimeler

Soliton çözümleri, sığ su, doğrusal olmayan dalga dinamiği, karanlık soliton.

Kaynakça

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