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TMF, 2003, Volume 134, Number 1, Pages 46–54 (Mi tmf139)  

This article is cited in 13 scientific papers (total in 13 papers)

Semiclassical $\bar\partial$-Method: Generating Equations for Dispersionless Integrable Hierarchies

L. V. Bogdanova, B. G. Konopelchenkob, L. Martínez Alonsoc

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Lecce University
c Universidad Complutense, Departamento de Fisica Teorica II

Abstract: We use the semiclassical $\bar\partial$-dressing method to derive compact generating equations for dispersionless hierarchies. The considered illustrative examples are the dispersionless Kadomtsev–Petviashvili and two-dimensional Toda lattice hierarchies.

Keywords: semiclassical limit, $\bar\partial$-method, $\tau$-function

DOI: https://doi.org/10.4213/tmf139

Full text: PDF file (219 kB)
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English version:
Theoretical and Mathematical Physics, 2003, 134:1, 39–46

Bibliographic databases:


Citation: L. V. Bogdanov, B. G. Konopelchenko, L. Martínez Alonso, “Semiclassical $\bar\partial$-Method: Generating Equations for Dispersionless Integrable Hierarchies”, TMF, 134:1 (2003), 46–54; Theoret. and Math. Phys., 134:1 (2003), 39–46

Citation in format AMSBIB
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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. Bogdanov LV, Konopelchenko BG, “Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type”, Physics Letters A, 330:6 (2004), 448–459  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Bogdanov LV, Konopelchenko BG, “Nonlinear Beltrami equation and tau-function for dispersionless hierarchies”, Physics Letters A, 322:5–6 (2004), 330–337  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. Bogdanov LV, Konopelchenko BG, “On the partial derivative-dressing method applicable to heavenly equation”, Physics Letters A, 345:1–3 (2005), 137–143  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    5. Bogdanov LV, Konopelchenko BG, “On dispersionless BKP hierarchy and its reductions”, Journal of Nonlinear Mathematical Physics, 12 (2005), 64–73, Suppl. 1  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Ferapontov EV, Khusnutdinova KR, Tsarev SP, “On a class of three-dimensional integrable Lagrangians”, Communications in Mathematical Physics, 261:1 (2006), 225–243  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Kanehisa Takasaki, “Dispersionless Hirota Equations of Two-Component BKP Hierarchy”, SIGMA, 2 (2006), 057, 22 pp.  mathnet  crossref  mathscinet  zmath
    8. Bogdanov, LV, “On the heavenly equation hierarchy and its reductions”, Journal of Physics A-Mathematical and General, 39:38 (2006), 11793  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    9. Dunajski, M, “Twistor theory and differential equations”, Journal of Physics A-Mathematical and Theoretical, 42:40 (2009), 404004  crossref  mathscinet  zmath  isi  scopus  scopus
    10. Burovskiy P.A., Ferapontov E.V., Tsarev S.P., “Second-Order Quasilinear PDEs and Conformal Structures in Projective Space”, Internat J Math, 21:6 (2010), 799–841  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    11. Ferapontov E.V., Odesskii A.V., Stoilov N.M., “Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions”, J Math Phys, 52:7 (2011), 073505  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    12. Takasaki K., “Differential Fay Identities and Auxiliary Linear Problem of Integrable Hierarchies”, Exploring New Structures and Natural Constructions in Mathematical Physics, Advanced Studies in Pure Mathematics, 61, eds. Hasegawa K., Hayashi T., Hosono S., Yamada Y., Math Soc Japan, 2011, 387–441  mathscinet  zmath  isi
    13. Grinevich P.G., Santini P.M., “Holomorphic Eigenfunctions of the Vector Field Associated with the Dispersionless Kadomtsev-Petviashvili Equation”, J. Differ. Equ., 255:7 (2013), 1469–1491  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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