Birleştirilmiş KdV-mKdV Denkleminin Yaklaşık Analitik Çözümleri Üzerine Bir Çalışma

Year 2020, Volume: 10 Issue: 4, 917 - 924, 15.10.2020

Turgut Ak Bilge Inan

https://doi.org/10.17714/gumusfenbil.678682

Abstract

Bu çalışmada, araştırma indirgenmiş diferansiyel dönüşüm metodunu (İDDM)
kullanarak birleştirilmiş KdV-mKdV denkleminin solitary dalga çözümleri üzerine
odaklanmaktadır. Önerilen metodun geçerliliğini kanıtlamak için, mutlak hata
vasıtasıyla yaklaşık analitik çözümler ve tam çözümler karşılaştırılmıştır.
Elde edilen sonuçlar grafiklerle temsil edilmiştir. Zaman ve dispersiyon
parametresinin



















 analitik çözümler üzerindeki
etkileri araştırılmıştır. Sonuç olarak, uygulanan yöntemin benzer tipteki
denklemler için oldukça hassas ve başarılı olduğu söylenebilir.

Keywords

Birleştirilmiş KdV-mKdV Denklemi, Gardner Denklemi, İDDM, İndirgenmiş Diferansiyel Dönüşüm Metodu, Solitary Dalga

A Study on Approximate Analytic Solutions of the Combined KdV-mKdV Equation

Abstract

In this paper, the investigation
focuses on solitary wave solutions of the combined KdV-mKdV equation by using
reduced differential transform method (RDTM). To prove validity of the proposed
method, the approximate analytic solutions and exact solutions of the equation
are compared via absolute errors. The obtained results are represented by
graphics. The effects of the time and dispersion parameter



















 on analytic solutions are investigated. As a
result, it can be said that the applied method is quite precise and successful
for similar type equations.

Keywords

Combined KdV-mKdV Equation, Gardner Equation, RDTM, Reduced Differential Transform Method, Solitary Wave

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