δ̅-equations, integrable deformations of quasiconformal mappings and Whitham hierarchy
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2001
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Elsevier
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Abstract
It is shown that the dispersionless scalar integrable hierarchies and, in general, the universal hitham hierarchy are nothing but classes of integrable deformations of quasiconformal mappings on the plane. Examples of deformations of quasiconformal mappings associated with explicit solutions of the dispersionless KP hierarchy are presented.
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©2001 Elsevier Science B.V. All rights reserved.
We would like to thank Prof. E. Medina for carrying out the computer calculation of the coefficients in the second example of Section 4. B.K. is supported in part by COFIN 2000 “Sintesi” and L.M.A. by proyecto PB98-0821.