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TMF, 2002, Volume 133, Number 2, Pages 247–258 (Mi tmf394)  

This article is cited in 8 scientific papers (total in 8 papers)

Quasiconformal Mappings and Solutions of the Dispersionless KP Hierarchy

B. G. Konopelchenkoa, L. Martínez Alonsob, E. Medinac

a Lecce University
b Universidad Complutense, Departamento de Fisica Teorica II
c Universidad de Cadiz

Abstract:$\bar {\partial }$ 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: https://doi.org/10.4213/tmf394

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

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Citation: B. G. Konopelchenko, L. Martínez Alonso, E. Medina, “Quasiconformal Mappings and Solutions of the Dispersionless KP Hierarchy”, TMF, 133:2 (2002), 247–258; Theoret. and Math. Phys., 133:2 (2002), 1529–1538

Citation in format AMSBIB
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\paper Quasiconformal Mappings and Solutions of the Dispersionless KP Hierarchy
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\jour Theoret. and Math. Phys.
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\pages 1529--1538
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Konopelchenko, B, “Quasi-classical partial derivative-dressing approach to the weakly dispersive KP hi(e)rarchy”, Journal of Physics A-Mathematical and General, 36:47 (2003), 11837  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Alonso, LM, “Additional symmetries and solutions of the dispersionless KP hierarchy”, Journal of Mathematical Physics, 44:8 (2003), 3294  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Konopelchenko B, Moro A, “Integrable equations in nonlinear geometrical optics”, Studies in Applied Mathematics, 113:4 (2004), 325–352  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Wu, D, “The partial derivative-approach to the dispersionless (2+1)-Harry Dym hierarchy”, Journal of Physics A-Mathematical and General, 38:27 (2005), 6167  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Pavlov, MV, “Hydrodynamic chains and the classification of their Poisson brackets”, Journal of Mathematical Physics, 47:12 (2006), 123514  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Pavlov, MV, “Classification of integrable hydrodynamic chains and generating functions of conservation laws”, Journal of Physics A-Mathematical and General, 39:34 (2006), 10803  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Pavlov M.V., “The Kupershmidt hydrodynamic chains and lattices”, International Mathematics Research Notices, 2006, 46987  mathscinet  zmath  isi  elib
    8. Gibbons, J, “Hamiltonian Structures of Reductions of the Benney System”, Communications in Mathematical Physics, 287:1 (2009), 291  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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