Nalini Joshi 2009 J. Phys. A: Math. Theor. 42 022001 doi:10.1088/1751-8113/42/2/022001
Direct 'delay' reductions of the Toda equation
FREE ARTICLENalini Joshi
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A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differential-difference equations, sometimes referred to as delay-differential equations. The representative equation of this class is hypothesized to be a new version of one of the classical Painlevé equations. The Lax pair associated with this equation is obtained, also by reduction.
- PACS
- MSC
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82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
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- Dates
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Issue 2 (16 January 2009)
Received 7 September 2008, in final form 28 October 2008
Published 2 December 2008
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Direct 'delay' reductions of the Toda equation
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