A. I. Zenchuk, S. V. Manakov, “The dual $\overline \partial$-problem, $(2+1)$-dimensional nonlinear evolution equations and their reductions”, TMF, 105:3 (1995), 371–382; Theoret. and Math. Phys., 105:3 (1995), 1490

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Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 105, Number 3, Pages 371–382 (Mi tmf1381)

This article is cited in 5 scientific papers (total in 5 papers)

The dual $\overline \partial$-problem, $(2+1)$-dimensional nonlinear evolution equations and their reductions

A. I. Zenchuk, S. V. Manakov

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Full-text PDF (980 kB) Citations (5)

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Abstract: The dual $\overline \partial$-problem with arbitrary normalization is used for compact description of integrable nonlinear PDE's with singular dispersion relations in $(2+1)$-dimensions. Various symmetry reductions and corresponding Lax representations for them are found. The singular KP-hierarchy and Schrödinger equation with magnetyic field are considered as the examples.

Received: 09.02.1995

English version:
Theoretical and Mathematical Physics, 1995, Volume 105, Issue 3, Pages 1490–1499
DOI: https://doi.org/10.1007/BF02070869

Bibliographic databases:

Language: Russian

Citation: A. I. Zenchuk, S. V. Manakov, “The dual $\overline \partial$-problem, $(2+1)$-dimensional nonlinear evolution equations and their reductions”, TMF, 105:3 (1995), 371–382; Theoret. and Math. Phys., 105:3 (1995), 1490–1499

Citation in format AMSBIB

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\pages 371--382

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\transl

\jour Theoret. and Math. Phys.

\yr 1995

\vol 105

\issue 3

\pages 1490--1499

\crossref{https://doi.org/10.1007/BF02070869}

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Linking options:

https://www.mathnet.ru/eng/tmf1381

https://www.mathnet.ru/eng/tmf/v105/i3/p371

This publication is cited in the following 5 articles:

Zenchuk, AI, “Multidimensional hierarchies of (1+1)-dimensional integrable partial differential equations. Nonsymmetric partial derivative-dressing”, Journal of Mathematical Physics, 41:9 (2000), 6248
A. I. Zenchuk, “Miura-type transformations of nonlinear partial differential equations integrable by the $\bar\partial$-problem method”, Theoret. and Math. Phys., 119:1 (1999), 431–437
L. V. Bogdanov, Analytic-Bilinear Approach to Integrable Hierarchies, 1999, 156
A. I. Zenchuk, “Some generalizations of the 2-dimensional Toda chain and $\operatorname{sh}$-Gordon equation”, Theoret. and Math. Phys., 110:2 (1997), 183–189
A. I. Zenchuk, “On the integration of some classes of weakly deformed nonlinear Schrödinger equations”, Jetp Lett., 66:3 (1997), 222

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

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Abstract page:	384
Full-text PDF :	135
References:	63
First page:	1

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