Birleştirilmiş KdV-mKdV Denkleminin Yaklaşık Analitik Çözümleri Üzerine Bir Çalışma

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.

Anahtar Kelimeler:

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

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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