The staircase method: integrals for periodic reductions of integrable lattice equations

Details The staircase method: integrals for periodic reductions of integrable lattice equations The staircase method: integrals for periodic reductions of integrable lattice equations

2010-05-12

arxiv.org/abs/1005.2071v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

40 pages, 23 Figures

Scientific paper

We show, in full generality, that the staircase method provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the QD-algorithm, and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r

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