2010/02/28 by Ismagil Habibullin, Natalya Zheltukhina, Alfia Sakieva · 1 citation
Mathematics · Medicine · Physics and Astronomy · #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Nonlinear Waves and Solitons #nlin.SI
paper · pdf · doi:10.1088/1751-8113/43/43/434017
published as J. Phys. A: Math. Theor. 43 (2010) 434017 (14pp) · 19 pages
openalex publication_date 2010/10/12 · arxiv created 2011/02/08 · arxiv updated 2011/02/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
A differential-difference equation with unknown t ( n , x ) depending on the continuous and discrete variables x and n is studied. We call an equation of such kind Darboux integrable if there exist two functions (called integrals) F and I of a finite number of dynamical variables such that D x 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). It is proved that the integrals can be brought to some canonical form. A method of construction of an explicit formula for a general solution to Darboux-integrable chains is discussed and such solutions are found for a class of chains.