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2+1 BOYUTTA YENİ İNTEGRE EDİLEBİLİR HAMİLTONIAN SİSTEMLER

A NEW 2+1-DIMENSIONAL HAMILTONIAN INTEGRABLE SYSTEM

Journal Name:

  • Sigma Mühendislik ve Fen Bilimleri Dergisi

Publication Year:

  • 2009

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Keywords (Original Language):

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Abstract (2. Language): 
It is shown that a new 2+1-dimensional second-order partial differential equation, when written as a first-order nonlinear evolutionary system, admits bi-Hamiltonian structure. Therefore, by Magri’s theorem it is a completely integrable system. For this system a Lagrangian is introduced and Dirac’s theory is applied in order to obtain first Hamiltonian structure. Then recursion operator is constructed and finally the second Hamiltonian structure for this system is obtained. Jacobi identity for the Hamiltonian structure is proved by using Olver’s method. Thus, it is an example of a completely integrable system in three dimensions.
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Abstract (Original Language): 
Yeni 2+1 boyutlu ikinci mertebeden kismi türevli diferansiyel denklem, birinci mertebe lineer olmayan değişim sistemi olarak yazıldığında, bu yeni sistemin bi-Hamiltonian yapıya sahip olduğu gösterilmiştir. Böylece Magri teoremine göre tamamen integere edilebilir bir sistem elde edilmiştir. Bu sistem için Lagrangian elde edilmiş, ve birinci Hamiltonian yapıyı elde etmek için Dirac teori uygulanmıştır. Sistem için tekrarlama (recursion) operatorü kurulmuş ve son olarak ikinci Hamiltonian yapı elde edilmiştir. Hamiltonian yapılar için Jacobi özdeşliği Olver’in metodu kullanılarak ispatlanmıştır. Böylece yeni denklem üç boyutta tamamen integre edilebilir sitemlere bir örnek teşkil etmektedir.
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  • Turkish

REFERENCES

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