M Bruschi et al 2009 J. Phys. A: Math. Theor. 42 475202 doi:10.1088/1751-8113/42/47/475202
M Bruschi1,2, F Calogero1,2 and R Droghei3
Show affiliationsAn isochronous system is introduced by modifying the Nth ODE of the stationary Burgers hierarchy, and then, by investigating its behaviour near its equilibria, neat Diophantine relations are identified, involving (well-known) polynomials of arbitrary degree having integer zeros, or equivalently matrices the determinants of which yield such polynomials. The basic idea to arrive at such relations is not new, but the specific application reported in this paper is new, and it is likely to open the way to several analogous new findings.
02.10.De Algebraic structures and number theory
30D30 Meromorphic functions, general theory
11C20 Matrices, determinants (See also 15A36)
34M55 Painlevé and other special equations; classification, hierarchies; isomonodromic deformations
Issue 47 (27 November 2009)
Received 18 July 2009
Published 4 November 2009
M Bruschi et al 2009 J. Phys. A: Math. Theor. 42 475202
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