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Journal of Mathematical Physics : On the classification of Darboux integrable chains

By Ismagil Habibullin, Natalya Zheltukhina, and Aslý Pekcan

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Book Id: WPLBN0002169547
Format Type: PDF eBook :
File Size: Serial Publication
Reproduction Date: 9 October 2008

Title: Journal of Mathematical Physics : On the classification of Darboux integrable chains  
Author: Ismagil Habibullin, Natalya Zheltukhina, and Aslý Pekcan
Volume: Issue : October 2008
Language: English
Subject: Science, Physics, Natural Science
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Journal of Mathematical Physics Collection
Historic
Publication Date:
Publisher: American Institute of Physics

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Natalya Zheltukhina, And Aslý Pekca, I. H. (n.d.). Journal of Mathematical Physics : On the classification of Darboux integrable chains. Retrieved from http://community.ebooklibrary.org/


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Description: We study a differential-difference equation of the form tx(n+1) = f(t(n),t(n+1),tx(n)) with unknown t = t(n,x) depending on x and n. The equation is called a Darboux integrable if there exist functions F (called an x-integral) and I (called an n-integral), both of a finite number of variables x,t(n),t(n±1),t(n±2),…,tx(n),txx(n),…, such that DxF = 0 and DI = I, where Dx is the operator of total differentiation with respect to x and D is the shift operator: Dp(n) = p(n+1). The Darboux integrability property is reformulated in terms of characteristic Lie algebras that give an effective tool for classification of integrable equations. The complete list of equations of the form above admitting nontrivial x-integrals is given in the case when the function f is of the special form f(x,y,z) = z+d(x,y).

 

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