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Initial value problems for lattice equations

journal contribution
posted on 29.03.2022, 03:44 by Pieter Van Der KampPieter Van Der Kamp
We describe how to pose straight band initial value problems for lattice equations defined on arbitrary stencils. In finitely many directions, we arrive at discrete Goursat problems and in the remaining directions we find Cauchy problems. Next, we consider (s1, s2)-periodic initial value problems. In the Goursat directions, the periodic solutions are generated by correspondences. In the Cauchy directions, assuming the equation to be multi-linear, the periodic solution can be obtained uniquely by iteration of a particularly simple mapping, whose dimension is a piecewise linear function of s1, s2. © 2009 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. Thanks are due to both Reinout Quispel and James Atkinson for valuable discussions.

History

Publication Date

16/09/2009

Journal

Journal of Physics A: Mathematical and Theoretical

Volume

42

Issue

40

Article Number

404019

Pagination

16p.

Publisher

IOP Publishing

ISSN

1751-8113

Rights Statement

© 2009 IOP Publishing Ltd.

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