2017

Farklı Metodlar ile Schamel-KdV denkleminin Analitik Çözümleri: Tozlu Uzay Plazmasına Uygulanması

Içerisinde negatif ve pozitif yüklü tozların yanında dagılmı¸s izotermal olmayan ˘ elektronlar barındıran tozlu uzay plazmasındaki dalganın özellikleri, Schamel-KdV denklemlerinin tam ilerleyen dalga çözümleri kullanılarak incelenmi¸stir. Analitik çözümler, (G ′/G)-geni¸sleme methodunun farklı tipleri ve direk integrasyon kullanılarak bulunmu¸stur. ˙Ion-akustik dalgasının lineer olmayan dinamigi, faz hızının ˘ Vp, plazma parametreleri α, σ, ve σd, ve kaynak terimi µ’nun farklı degerleri için çalı¸sılmı¸stır. Bunun sonu- ˘ cunda, farklı methodlardan elde edilen farklı analitik çözümler ile farklı türden dalgalar gözlemledik ve süreksiz, ¸sok veya soliton dalgası bulduk. Aynı zamanda, yukarıda verilen parametrelerin plazma içerisinde soliton tipi dalgaların olu¸smasında önemli bir rol oynadıgı sonucuna ula¸sılmı¸stır. Bu parametrelere ba ˘ glı olarak süreksiz dalga plazma ˘ parametrelerinin ve faz hızının belli degerleri için soliton tipi bir dalgaya donü¸sür. Bun- ˘ lara ek olarak, Schamel-KdV denkleminin tam analitik çözümleri, verilen bir plazmanın özelliklerinin ve dalga tiplerinin anla¸sılması için farklı plazma sistemlerine de uygulanabilir.

Analytic Solutions of the Schamel-KdV Equation by Using Different Methods: Application to a Dusty Space Plasma

The wave properties in a dusty space plasma consisting of positively and negatively charged dust as well as distributed nonisothermal electrons are investigated by using the exact traveling wave solutions of the Schamel-KdV equation. The analytic solutions are obtained by the different types (G ′/G)-expansion methods and direct integration. The nonlinear dynamics of ion-acoustic waves for the various values of phase speed Vp, plasma parameters α, σ, and σd, and the source term µ are studied. We have observed different types of waves from the different analytic solutions obtained from the different methods. Consequently, we have found the discontinuity, shock or solitary waves. It is also concluded that these parameters play an important role in the presence of solitary waves inside the plasma. Depending on plasma parameters, the discontinuity wave turns into solitary wave solution for the certain values of the phase speed and plasma parameters. Additionally, exact solutions of the Schamel-KdV equation may also be used to understand the wave types and properties in the different plasma systems.

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