Bazı lineer olmayan diferansiyel denklemlerin tam çözümleri için metotlar

Kısmi diferansiyel denklemler fen, mühendislik ve diğer çeşitli uygulamalarda karşılaşılan olayların evrimini tanımlamada bizlere yardımcı olduklarından genel olarak matematiğin gelişiminde temel rol oynamaktadırlar. Bu çalışmada bir bilgisayar cebiri sistemi olan Maple yardımıyla lineer olmayan kısmi diferansiyel denklemlerin çözümleri için farklı yaklaşımlar takip edeceğiz. Bunun için son zamanlarda geliştirilen ve lineer olmayan kısmi diferansiyel denklemlerin hareketli dalga çözümlerini elde etmemize izin veren üç metot, tanh-fonksiyonu metodu, deneme fonksiyonu metodu ve en basit denklem metodu, ele alınmaktadır. Bu metotların kullanımı çeşitli lineer olamayan evrim denklemlerine uygulanarak açıklanmıştır ve elde edilen çözümlerden bazılarının grafikleri verilmiştirTheory of partial differential equations plays a central role within the general advancement of mathematics, since they help us to describe the evolution of many phenomena in various fields of science, engineering, and numerous other applications. In this work, we follow different approaches to solve nonlinear partial differential equations with the aid of computer algebra system, Maple. We consider recently developed three methods, namely tanh-function method, trial function method and simplest equation method, which allow us to construct travelling wave solutions of nonlinear partial differential equations. The use of these methods is illustrated by applying them to a variety of nonlinear evolution equations and graphs are drawn for some of the obtained solutions

Thermodynamic phase diagram stability, electronic and thermoelectric properties of the half-Heusler KMgP [111] films

The mechanical, electronic and thermoelectric calculations of the KMgP half-Heusler compound and its [111] thin films have been done in the framework of density functional theory. The KMgP bulk has mechanical stability in the static and dynamic viewpoints, and it has the p-type semiconductor behavior with the 1.1-eV energy gap. The KMgP in the bulk phase is a relatively good thermoelectric compound with a figure of merit of 0.7 above the room temperature. The KMgP [111] film has three K-, Mg- and P-terminations. The last one has 100% spin polarization at the Fermi level, which is referred to as the fully half-metallic behavior. The thermoelectric efficiency of the P-termination case in the up spin is more than that of the bulk structure. The figure of merit for this termination is about one at room temperature, which made it the right candidate for thermoelectric applications