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On the classification of Darboux integrable chains

Date
2008
Author
Habibullin, İsmagil
PEKCAN, ASLI
Zheltukhina, Natalya
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Abstract
We study a differential-difference equation of the form t(x)(n + 1)=f (t(n),t(n + 1), t(x)(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),..., t(x)(n), t(xx)(n),..., such that DxF=0 and DI=I, where D-x 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). (C) 2008 American Institute of Physics. [DOI: 10.1063/1.2992950]
URI
http://hdl.handle.net/20.500.12627/158415
https://doi.org/10.1063/1.2992950
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Creative Commons Lisansı

İstanbul Üniversitesi Akademik Arşiv Sistemi (ilgili içerikte aksi belirtilmediği sürece) Creative Commons Alıntı-GayriTicari-Türetilemez 4.0 Uluslararası Lisansı ile lisanslanmıştır.

DSpace software copyright © 2002-2016  DuraSpace
Contact Us | Send Feedback
Theme by 
Atmire NV