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

journal contribution
posted on 29.03.2022, 03:27 by DT Tran, PHVD Kamp, Gilles QuispelGilles Quispel
Closed form expressions in terms of multi-sums of products have been given in Tran et al (2009 J. Phys A: Math. Theor. 42 225201) and van der Kamp et al (2007 J. Phys. A: Math. Theor. 39 12789-98) of integrals of sine-Gordon, modified Korteweg-de Vries and potential Korteweg-de Vries maps obtained as so-called (p, -1)-travelling 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. © 2011 IOP Publishing Ltd.

Funding

This research has been funded by the Australian Research Council through the Centre of Excellence for Mathematics and Statistics of Complex Systems. DTT acknowledges the support of two scholarships, one from La Trobe University and the other from the Endeavour IPRS programme.

History

Publication Date

21/06/2011

Journal

Journal of Physics A: Mathematical and Theoretical

Volume

44

Issue

29

Article Number

295206

Pagination

13p.

Publisher

IOP Publishing

ISSN

1751-8113

Rights Statement

© 2011 IOP Publishing Ltd.