The Whitham hierarchies: reductions and hodograph solutions
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2003
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IOP Publishing
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Abstract
A general scheme for analysing reductions of Whitham hierarchies is presented. It is based on a method for determining the S-function by means of a system of first-order partial differential equations. Compatibility systems of differential equations characterizing both reductions and hodograph solutions of Whitham hierarchies are obtained. The method is illustrated by exhibiting solutions of integrable models such as the dispersionless Toda equation (heavenly equation) and the generalized Benney system.
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© 2003 IOP Publishing Ltd.
This work originated during the stay of the authors at the Isaac Newton Institute for the Mathematical Sciences of Cambridge University as participants of the programme ‘Integrable Systems’. The authors are grateful to the organizers for the support provided. They also acknowledge S P Tsarev and A Mikhailov for useful comments and conversations. The work is partially supported by CICYT proyecto PB98–0821.