Asymptotic formulas and numerical estimations for eigenvalues of SturmLiouville problems having singular potential functions, with Dirichlet boundary conditions, are obtained. This study gives a comparison between the eigenvalues obtained by the asymptotic and the numerical methods.
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.
In this study, Kudryashov Method is used to find the wave solutions of the Gardner equation, fifth order Caudrey-Dodd-Gibbon equation and Sawada-Kotera equation, which are non-linear partial differential equations used as a mathematical model in the physics science field and engineering applications. The exact solutions obtained are compared with the results in the literature and hyperbolic type and soliton solutions are obtained.
Bu çalışmada, lineer olmayan Drinfeld-Sokolov denklem sistemi ve Modifiye-Benjamin-Bona-Mahony denkleminin pertürbatif çözümleri, homotopi pertürbasyon yöntemi kullanılarak elde edilmiştir. Denklemlerin pertürbatif çözümleri için üç iterasyon yapılmıştır. Birinci iterasyonlar kullanılarak her iki denklem için de basit dallanma noktaları hesaplanmıştır. İkinci iterasyonlar için basit dallanma noktasının yalnızca Drinfeld-Sokolov denklem sisteminde olduğu görülmüştür.
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