Calogero-Bogoyavlenskii-Schiff denkleminin analitik çözümleri

Abstract

Kısmi Diferansiyel denklemlerin analitik çözümleri, kuantum mekanik ve plazma fiziği gibi alanlarda, açığa çıkmamış olayların açıklanmasında fayda sağlamaktadır. Bu çalışmada, lineer olmayan kısmi türevli Calogero-Bogoyavlenskii-Schiff (CBS) diferansiyel denkleminin analitik çözümlerini bulmak için Homojen Denge Metodundan yararlanılmıştır. Homojen Denge Metodunun Calogero-Bogoyavlenskii-Schiff denklemine uygulanmasıyla elde edilen analitik çözümler literatürde bulunan sonuçlarla karşılaştırılmış ve literatürde bulunan çözümlerle uyumlu hiperbolik ve trigonometrik tipten fonksiyonlar elde edilmiştir.

Keywords

• Calogero–Bogoyavlenskii-Schiff (CBS) denklemi
• homojen denge metodu
• analitik çözüm

Analytical solutions of Calogero-Bogoyavlenskii-Schiff equation

Abstract

Analytical solutions of Partial Differential equations are useful in explaining unrevealed events in areas such as quantum mechanics and plasma physics. In this study, the Homogeneous Balance Method is used to find analytical solutions of the nonlinear partial differential Calogero-Bogoyavlenskii-Schiff (CBS) differential equation. Analytical solutions obtained by applying the Homogeneous Balance Method to the Calogero-Bogoyavlenskii-Schiff equation are compared with the results found in the literature, and hyperbolic and trigonometric type functions that are compatible with the solutions in the literature are obtained.

Keywords

• Calogero–Bogoyavlenskii-Schiff (CBS) equation
• homogeneous balance method
• analytical solution

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