Solution of the (2+1) Dimensional Breaking Soliton Equation by Using Two Different Methods

Abstract

In this study, the direct integration and homotopy perturbation method are used for the non-linear partial differential (2+1) dimensional breaking soliton equation. By assigning some special values to the constants in the solutions of the (2+1) dimensional breaking soliton equation, The direct integration was used for obtaining the known solution in the literature in practical and shortest way. By using the homotopy perturbation method with one iteration, it was obtained same type solution to (2+1) dimensional breaking soliton equation. Similarly, same type solutions could be done in different methods such as (G'/G)-expansion method.

Calogero-Bogoyavlenskii-Schiff denkleminin analitik çözümleri

“…Bu denklemlerin çözümlerini elde etmek için nümerik ve analitik metotlar geliştirilmiştir [5]. Bu metotlardan; Varyasyonel İterasyon Metot [6,7], Homotopi Analiz Metot [8], Homotopi Pertürbasyon Metot [9][10][11], Adomian Ayrışım Metot [12], Homojen Denge Metot [13][14][15][16][17][18][19][20][21][22][23][24] ve diğerleri son yirmi yılda litaratürde bulunan çalışmalardandır. Lineer olmayan denklemlerin çözümlerine Homojen Denge Metodun kullanımıyla hızlı ve analitik sonuçlara ulaşılmaktadır.…”