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GEOMETRY OF INTEGRABLE LATTICE EQUATIONS AND THEIR REDUCTIONS

Part of: Surfaces and higher-dimensional varieties Difference and functional equations Difference equations

Published online by Cambridge University Press:  17 May 2019

MATTHEW NOLAN Open the ORCID record for MATTHEW NOLAN [Opens in a new window]
MATTHEW NOLAN*
Affiliation:
School of Mathematics and Statistics, University of Sydney, Camperdown, NSW 2006, Australia email m.nolan@maths.usyd.edu.au
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Abstract

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Keywords

secondary 14J17singularitiesblow uplinear equationsq-difference equationspartial difference equationslattice equationsPainlevé equation

MSC classification

Primary: 14J17: Singularities
Secondary: 39A06: Linear equations 39A14: Partial difference equations
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 100 , Issue 1 , August 2019 , pp. 168 - 169
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Footnotes

Thesis submitted to The University of Sydney in April 2017; degree approved on 17 September 2018; supervisor: Nalini Joshi.

References

Adler, V. E., Bobenko, A. I. and Suris, Y. B., ‘Classification of integrable equations on quad-graphs. The consistency approach’, Commun. Math. Phys. 233(3) (2003), 513–543.Google Scholar
Joshi, N., Lobb, S. and Nolan, M., ‘Constructing initial value spaces of lattice equations’, Preprint, 2018, arXiv:1807.06162.Google Scholar
Sakai, H., ‘Rational surfaces associated with affine root systems and geometry of the Painlevé equations’, Commun. Math. Phys. 220(1) (2001), 165–229.Google Scholar