Wave Solution Analysis of a Nonlinear Mathematical Model on Fluid Mechanics

Öz

This study obtains some wave solutions of the B-type Kadomtsev Petviashvili equation by applying the modified exponential function method (MEFM). Thanks to this method, the exact solutions of the non-linear partial differential equations will be obtained and there will be an opportunity to examine the physical structure of these solutions. Due to the nature of MEFM, two different cases are presented here that have been analyzed to obtain more solutions in this structure. More wave solutions can be obtained by analyzing different situations. When the resulting solutions are analyzed, hyperbolic, trigonometric, and rational functions are observed. It has been checked whether the solution functions found with Wolfram Mathematica software provide the B type Kadomtsev Petviashvili equation and graphs simulating the wave solution behavior with the determined appropriate parameters are presented.

Anahtar Kelimeler

• Modified Exponential Function Method (MEFM)
• B-type Kadomtsev Petviashvili Equation
• Wave Solutions
• Geliştirilmiş Üstel Fonksiyon Metodu (GÜFM)
• B tipi Kadomtsev Petviashvili
• Dalga Çözümleri

Öz

Bu çalışmada, modifiye edilmiş üstel fonksiyon metodu uygulanarak B tipi Kadomtsev Petviashvili denkleminin bazı dalga çözümleri elde edilmiştir. Modifiye edilmiş üstel fonksiyon yönteminin doğası gereği, bu yapıdaki çözümlerden daha fazla elde etmek için incelenilmiş olan iki farklı durum burada sunulmuştur. Farklı durumlar da incelenerek daha fazla dalga çözümü elde edilebilir. Ortaya çıkan çözümler analiz edildiğinde hiperbolik, trigonometrik ve rasyonel fonksiyonlar gözlemlenmiştir. Wolfram Mathematica yazılımı ile bulunan çözüm fonksiyonlarının B tipi Kadomtsev Petviashvili denklemini sağlayıp sağlamadığı kontrol edilmiş ve belirlenen uygun parametrelerle dalga çözümünün üç boyutlu kontur, yoğunluk ve iki boyutlu grafiklerin analizi sunulmuştur.

Anahtar Kelimeler

• Geliştirilmiş Üstel Fonksiyon Metodu (GÜFM)
• B tipi Kadomtsev Petviashvili
• Dalga Çözümleri

Kaynakça

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