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

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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 134, Number 1, Pages 46–54
DOI: https://doi.org/10.4213/tmf139 (Mi tmf139)

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

Semiclassical

¯ \partial

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

L. V. Bogdanov^a, B. G. Konopelchenko^b, L. Martínez Alonso^c

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

Full-text PDF (219 kB) Citations (13)

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

Abstract: We use the semiclassical

¯ \partial

$\bar\partial$ -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,

¯ \partial

$\bar\partial$ -method,

τ

$\tau$ -function.

English version:
Theoretical and Mathematical Physics, 2003, Volume 134, Issue 1, Pages 39–46
DOI: https://doi.org/10.1023/A:1021863522034

Bibliographic databases:

Language: Russian

Citation: L. V. Bogdanov, B. G. Konopelchenko, L. Martínez Alonso, “Semiclassical

¯ \partial

$\bar\partial$ -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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\transl

\jour Theoret. and Math. Phys.

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Linking options:

https://www.mathnet.ru/eng/tmf139

https://doi.org/10.4213/tmf139

https://www.mathnet.ru/eng/tmf/v134/i1/p46

This publication is cited in the following 13 articles:

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
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
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
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
Dunajski, M, “Twistor theory and differential equations”, Journal of Physics A-Mathematical and Theoretical, 42:40 (2009), 404004
Ferapontov EV, Khusnutdinova KR, Tsarev SP, “On a class of three-dimensional integrable Lagrangians”, Communications in Mathematical Physics, 261:1 (2006), 225–243
Kanehisa Takasaki, “Dispersionless Hirota Equations of Two-Component BKP Hierarchy”, SIGMA, 2 (2006), 057, 22 pp.
Bogdanov, LV, “On the heavenly equation hierarchy and its reductions”, Journal of Physics A-Mathematical and General, 39:38 (2006), 11793
Bogdanov LV, Konopelchenko BG, “On the partial derivative-dressing method applicable to heavenly equation”, Physics Letters A, 345:1–3 (2005), 137–143
Bogdanov LV, Konopelchenko BG, “On dispersionless BKP hierarchy and its reductions”, Journal of Nonlinear Mathematical Physics, 12 (2005), 64–73, Suppl. 1
Bogdanov LV, Konopelchenko BG, “Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type”, Physics Letters A, 330:6 (2004), 448–459
Bogdanov LV, Konopelchenko BG, “Nonlinear Beltrami equation and tau-function for dispersionless hierarchies”, Physics Letters A, 322:5–6 (2004), 330–337
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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