BibTex format
@article{Gibbons:2011,
author = {Gibbons, J},
journal = {Computational Methods and Function Theory},
pages = {671--684},
title = {Constructing Benney Reductions associated with cyclic (n,s) Curves.},
volume = {11},
year = {2011}
}
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Citation
RIS format (EndNote, RefMan)
TY - JOUR
AB - Benney's equations admit 'reductions' to systems of dispersionless pdes with only finitely many N dependent variables. These reductions are parametrisedby conformal mappings from the half-plane to the half-plane minus N slits.A large family of these can be constructed as Schwartz-Christoffel mappings;an important subclass of these reduce to integrals of a second kind differential on an algebraic curve. Particular examples of these have beenconstructed; in particular there are 2 different constructions for the caseof a hyperelliptic curve. Other particular examples have been worked out,and the overall structure is similar to the hyperelliptic case, though thereare differences of detail. It is thus important to find the general structureof these, independently of the particular curve being studied. We use theFay Prime Form to investigate this, and sketch how this approach could be applied to general cyclic (n,s) curves.
AU - Gibbons,J
EP - 684
PY - 2011///
SN - 1617-9447
SP - 671
TI - Constructing Benney Reductions associated with cyclic (n,s) Curves.
T2 - Computational Methods and Function Theory
VL - 11
ER -