Journal of Non-linear Mathematical Physics

ISSN: 1402-9251
Volume 12, Issue Supplement 2, December 2005

Symmetries and Integrability of Difference Equations SIDE VI

Pages: 1 - 14
It is shown that discrete analogs of zc and log(z), defined via particular "integrable" circle patterns, have the same asymptotic behavior as their smooth counterparts. These discrete maps are described in terms of special solutions of discrete Painlevé-II equations, asymptotics of these solutions...
Christopher ATHORNE
Pages: 15 - 27
By associating polynomials and power series expansions with sln(C) modules we dscribe the theory of Padé approximants in terms of tensor products of representations and interpret their recurrence relations algebraically. The treatment links with the theory of Hirota derivatives and discrete integrable...
Pages: 28 - 35
First, we recall the algebro-geometric method of construction of finite field valued solutions of the discrete KP equation, and next we perform a reduction of dKP to the discrete 1D Toda equation.
Martin BOHNER, Christopher C TISDELL
Pages: 36 - 45
The theory of dynamic inclusions on a time scale is introduced, hence accommodating the special cases of differential inclusions and difference inclusions. Fixed point theory for set-valued upper semicontinuous maps, Green's functions, and upper and lower solutions are used to establish existence...
Pages: 95 - 136
We prove bispectral duality for the generalized Calogero­Moser­Sutherland systems related to configurations An,2(m), Cn(l, m). The trigonometric axiomatics of the Baker­Akhiezer function is modified, the dual difference operators of rational Madonald type and the Baker­Akhiezer functions related to...
Giuseppe GAETA, Decio LEVI, Rosaria MANCINELLI
Pages: 137 - 146
It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In this note we extend the approach to asymptotic symmetries for...
Pages: 155 - 168
A family of real Hamiltonian forms (RHF) for the special class of affine 1 + dimensional Toda field theories is constructed. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is generalized to infinite-dimensional Hamiltonian systems. We show that each of these RHF...
Pages: 223 - 230
For two-dimensional lattice equations the standard definition of integrability is that it should be possible to extend the map consistently to three dimensions, i.e., that it is "consistent around a cube" (CAC). Recently Adler, Bobenko and Suris conducted a search based on this principle, together...
Fabio MUSSO, Matteo PETRERA, Orlando RAGNISCO, Giovanni SATTA
Pages: 240 - 252
We consider a long­range homogeneous chain where the local variables are the geerators of the direct sum of N e(3) interacting Lagrange tops. We call this classical integrable model rational "Lagrange chain" showing how one can obtain it starting from su(2) rational Gaudin models. Moreover we construct...
Pages: 295 - 299
In this paper an extension of the q-deformed Volterra equation associated with linear rescaling to the general non-linear rescaling is obtained.