Results 11 to 20 of about 3,579,879 (270)
p-adic difference-difference Lotka-Volterra equation and ultra-discrete limit [PDF]
International Journal of Mathematics and Mathematical Sciences, 2001 We study the difference-difference Lotka-Volterra equations in p-adic number space and its p-adic valuation version. We point out that the structure of the space given by taking the ultra-discrete limit is the same as that of the p-adic valuation space ...
Shigeki Matsutani
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Symmetries of the Hirota Difference Equation [PDF]
, 2017 Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent variables of the equation is presented.
Pogrebkov, Andrei K.
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Entwined Paths, Difference Equations and the Dirac Equation [PDF]
, 2002 Entwined space-time paths are bound pairs of trajectories which are traversed in opposite directions with respect to macroscopic time. In this paper we show that ensembles of entwined paths on a discrete space-time lattice are simply described by coupled
E. Nelson +6 more
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Zero distribution of polynomials satisfying a differential-difference equation [PDF]
, 2013 In this paper we investigate the asymptotic distribution of the zeros of polynomials $P_{n}(x)$ satisfying a first order differential-difference equation.
Dominici, Diego, Van Assche, Walter
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On the discrete and continuous Miura Chain associated with the Sixth Painlevé Equation [PDF]
, 1999 A Miura chain is a (closed) sequence of differential (or difference) equations that are related by Miura or B\"acklund transformations. We describe such a chain for the sixth Painlev\'e equation (\pvi), containing, apart from \pvi itself, a Schwarzian ...
Ablowitz +25 more
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Some representations of the general solution to a difference equation of additive type
Advances in Difference Equations, 2019 The general solution to the difference equation xn+1=axnxn−1xn−2+bxn−1xn−2+cxn−2+dxnxn−1xn−2,n∈N0, $$x_{n+1}=\frac {ax_{n}x_{n-1}x_{n-2}+bx_{n-1}x_{n-2}+cx_{n-2}+d}{x_{n}x_{n-1}x_{n-2}},\quad n\in\mathbb{N}_{0}, $$ where a,b,c∈C $a, b, c\in\mathbb{C}$, d∈
Stevo Stević
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On the Difference Equation xn+1=xnxn-k/(xn-k+1a+bxnxn-k)
Abstract and Applied Analysis, 2012 We show that the difference equation xn+1=xnxn-k/xn-k+1(a+bxnxn-k),n∈ℕ0, where k∈ℕ, the parameters a, b and initial values x-i, i=0,k̅ are real numbers, can be solved in closed form considerably extending the results in the literature.
Stevo Stević +3 more
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Well-posedness of difference elliptic equation
Discrete Dynamics in Nature and Society, 1997 The exact with respect to step h∈(0,1] coercive inequality for solutions in Ch of difference elliptic equation is established.
Pavel E. Sobolevskii
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Representation of solutions of a solvable nonlinear difference equation of second order
Electronic Journal of Qualitative Theory of Differential Equations, 2018 We present a representation of well-defined solutions to the following nonlinear second-order difference equation $$x_{n+1}=a+\frac{b}{x_n}+\frac{c}{x_nx_{n-1}},\quad n\in\mathbb{N}_0,$$ where parameters $a, b, c$, and initial values $x_{-1}$ and $x_0 ...
Stevo Stevic +3 more
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A high order $q$-difference equation for $q$-Hahn multiple orthogonal polynomials [PDF]
, 2009 A high order linear $q$-difference equation with polynomial coefficients having $q$-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation is related to the number of orthogonality conditions that these polynomials ...
Abramowitz M. +10 more
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