The Soliton Solutions of the (1+1)-Dimensional Benjamin-Bona-Mahony (BBM) Equation Via the Modified New Kudryashov Method

Abstract

This study is aimed at obtaining analytical soliton solutions of the (1+1)-dimensional Benjamin-Bona-Mahony (BBM) equation with the new modified Kudryashov method. In the first stage, the model, which has the form of a nonlinear partial differential equation, is reduced to a nonlinear ordinary differential equation with the appropriate wave transformation. In the second stage, a system of linear algebraic equations is obtained by using the homogeneous equilibrium principle and the Riccati auxiliary differential equation, and the unknown parameters of the model examined are determined from the solution of this system. Depending on the different solution sets obtained, analytical soliton solutions are obtained and the main equation is checked. In the final stage, contour and three-dimensional graphic presentations are made to facilitate the physical interpretation of the solutions.

Keywords

• Wave Transformation
• Analytic Solution
• Partial Differential Equations
• Soliton Solution

(1+1)-Boyutlu Benjamin-Bona-Mahony (BBM) Denkleminin Modifiye Edilmiş Kudryashov Metodu ile Soliton Çözümleri

Abstract

Bu çalışma, (1+1)-boyutlu Benjamin-Bona-Mahony (BBM) denkleminin analitik soliton çözümlerinin modifiye edilmiş modifiye Kudryashov metodu ile elde edilmesine yöneliktir. Birinci aşamada, doğrusal olmayan kısmi türevli diferansiyel denklem formuna sahip olan model, uygun dalga dönüşümü ile doğrusal olmayan adi diferansiyel denkleme indirgenmektedir. İkinci aşamada ise, homojen denge prensibi ve Riccati yardımcı diferansiyel denklemi kullanılarak doğrusal cebirsel denklem sistemi elde edilerek bu sistemin çözümünden incelenen modelin bilinmeyen parametreleri belirlenmektedir. Elde edilen farklı çözüm setlerine bağlı olarak analitik soliton çözümleri elde edilerek ana denklemi sağlama kontrolü yapılmaktadır. Son aşamada ise çözümlerin fiziksel olarak yorumlanmasını kolaylaştırmak amacıyla kontur ve üç boyutlu grafik sunumları yapılmaktadır.

Keywords

• Dalga dönüşümü
• Analitik Çözüm
• Kısmi Diferansiyel Denklemler
• Soliton Çözümü

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