Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable Equations on Time Scales   Integrable systems are usually given in terms of functions of continuous
variables (on ${\mathbb R}$), functions of discrete variables (on ${\mathbb
Z}$) and recently in terms of functions of $q$-variables (on ${\mathbb
K}_{q}$). We formulate the Gel'fand-Dikii (GD) formalism on time scales by
using the delta differentiation operator and find more general integrable
nonlinear evolutionary equations. In particular they yield integrable equations
over integers (difference equations) and over $q$-numbers ($q$-difference
equations). We formulate the GD formalism also in terms of shift operators for
all regular-discrete time scales. We give a method to construct the recursion
operators for integrable systems on time scales. Finally, we give a trace
formula on time scales and then construct infinitely many conserved quantities
(Casimirs) of the integrable systems on time scales.

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The categories of this paper are: stat
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex