This article is cited in 10 papers

Quasiconformal Mappings and Solutions of the Dispersionless KP Hierarchy

B. G. Konopelchenko^a, L. Martínez Alonso^b, E. Medina<sup>c

a</sup> Lecce University
^b Universidad Complutense, Departamento de Fisica Teorica II
^c Universidad de Cadiz

Abstract: A $\bar {\partial }$ formalism for studying dispersionless integrable hierarchies is applied to the dispersionless KP (dKP) hierarchy. We relate this formalism to the theory of quasiconformal mappings on the plane and present some classes of explicit solutions of the dKP hierarchy.

Keywords: dispersionless hierarchies, quasiconformal mappings, $\bar {\partial }$ equations.

DOI: 10.4213/tmf394

 English version: Theoretical and Mathematical Physics, 2002, 133:2, 1529–1538

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