Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps

Details Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps

2010-10-18

arxiv.org/abs/1010.3471v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

24 pages

Scientific paper

Closed form expressions in terms of multi-sums of products have been given in \cite{Tranclosedform, KRQ} of integrals of sine-Gordon, modified Korteweg-de Vries and potential Korteweg-de Vries maps obtained as so-called $(p,-1)$-traveling wave reductions of the corresponding partial difference equations. We prove the involutivity of these integrals with respect to recently found symplectic structures for those maps. The proof is based on explicit formulae for the Poisson brackets between multi-sums of products.

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