On the classification of Darboux integrable chains
Author
Habibullin, I.
Zheltukhina, N.
Pekcan, A.
Date
2008Source Title
Journal of Mathematical Physics
Print ISSN
0022-2488
Electronic ISSN
1089-7658
Publisher
American Institute of Physics
Volume
49
Issue
10
Pages
102702-1 - 102702-39
Language
English
Type
ArticleItem Usage Stats
101
views
views
82
downloads
downloads
Abstract
We study differential-difference equation (d/dx) t (n+1,x) =f (t (n,x),t (n+1,x), (d/dx) t (n,x)) with unknown t (n,x) depending on continuous and discrete variables x and n. Equation of such kind is called Darboux integrable, if there exist two functions F and I of a finite number of arguments x, { t (n+k,x) } k=-∞ ∞, {(dk /d xk) t (n,x) } k=1 ∞, such that Dx F=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). Reformulation of Darboux integrability in terms of finiteness of two characteristic Lie algebras gives an effective tool for classification of integrable equations. The complete list of Darboux integrable equations is given in the case when the function f is of the special form f (u,v,w) =w+g (u,v). © 2009 American Institute of Physics.
Keywords
Difference EquationsDifferentiation
Integral equations
Lie algebras
Mathematical operators
Difference equations
Differentiation
Integral equations
Lie Algebras
Mathematical operators
Equations
Permalink
http://hdl.handle.net/11693/11637Published Version (Please cite this version)
http://dx.doi.org/10.1063/1.2992950Collections
Related items
Showing items related by title, author, creator and subject.
-
Fast multipole methods in service of various scientific disciplines
Gürel, Levent (IEEE, 2014)For more than two decades, several forms of fast multipole methods have been extremely successful in various scientific disciplines. Reduced complexity solutions are obtained for solving different forms of equations that ... -
Electrostatic interactions in charged nanoslits within an explicit solvent theory
Buyukdagli, S. (Institute of Physics Publishing, 2015)Within a dipolar Poisson-Boltzmann theory including electrostatic correlations, we consider the effect of explicit solvent structure on solvent and ion partition confined to charged nanopores. We develop a relaxation scheme ... -
Third order differential equations with fixed critical points
Adjabi, Y.; Jrad F.; Kessi, A.; Muǧan, U. (2009)The singular point analysis of third order ordinary differential equations which are algebraic in y and y′ is presented. Some new third order ordinary differential equations that pass the Painlevé test as well as the known ...