(2+1)-boyutlu Broer-Kaup-Kupershmidt denklemi ve Kolmogorov-Petrovskii-Piskunov denklemine modifiye edilmiş deneme denklem metodu

Abstract

Lineer olmayan problemlerin çözümünü bulmak için bilim insanları tarafından birçok yöntem geliştirilmiştir. Bu yazıda, modifiye edilmiş deneme denklem metodunun (MEDDM) genel yapısı tanıtılmış ve (2+1)-boyutlu Broer-Kaup-Kupershmidt (BKK), Kolmogorov-Petrovskii-Piskunov (KPP) denklemlerinin bazı tam çözümlerini bulmak için MEDDM kullanılmıştır. İlk olarak, hareketli dalga dönüşümü altında lineer olmayan kısmi diferansiyel denklemin (NLPDE) adi diferansiyel denkleme indirgenmesiyle bir cebirsel denklem sistemi elde edilmiştir. Elde edilen cebirsel denklem sistemleri çözülerek hareketli dalga çözümleri bulunur. Mathematica 9 programı kullanılarak, dalga çözümlerinin fiziksel davranışını analiz etmek için uygun parametreler için üç ve iki boyutlu grafikler çizilmiştir. MEDDM, bazı kısmi diferansiyel denklemlerin tam çözümlerini bulmada büyük önem taşımaktadır.

Keywords

• (2+1)-boyutlu BKK denklemi
• KPP denklemi
• hareketli dalga çözümü.

The modified trial equation method to the (2+1)-dimensional Broer-Kaup-Kupershmidt equation and Kolmogorov-Petrovskii-Piskunov equation

Abstract

Many methods have been developed by scientists to find solutions for nonlinear problems. In this paper, the general structure of the modified trial equation method (MTEM) is introduced, and MTEM is used to find some exact solutions of (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK), Kolmogorov-Petrovskii-Piskunov (KPP) equations. Firstly, an algebraic equation system is obtained by reducing the nonlinear partial differential equation (NLPDE) to the ordinary differential equation under the travelling wave transformation. Travelling wave solutions are found by solving the obtained algebraic equation systems. By using Mathematica 9 program, three and two dimensional graphs for suitable parameters were plotted to analyze the physical behavior of wave solutions. MTEM is of great importance in finding exact solutions of some partial differential equations.

Keywords

• (2+1)-dimensional BKK equation
• KPP equation
• travelling wave solution.

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