The dual $\overline \partial$-problem, $(2+1)$-dimensional nonlinear evolution equations and their reductions
Teoretičeskaâ i matematičeskaâ fizika, Tome 105 (1995) no. 3, pp. 371-382
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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.
@article{TMF_1995_105_3_a2,
author = {A. I. Zenchuk and S. V. Manakov},
title = {The dual $\overline \partial$-problem, $(2+1)$-dimensional nonlinear evolution equations and their reductions},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {371--382},
publisher = {mathdoc},
volume = {105},
number = {3},
year = {1995},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1995_105_3_a2/}
}
TY - JOUR AU - A. I. Zenchuk AU - S. V. Manakov TI - The dual $\overline \partial$-problem, $(2+1)$-dimensional nonlinear evolution equations and their reductions JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1995 SP - 371 EP - 382 VL - 105 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1995_105_3_a2/ LA - ru ID - TMF_1995_105_3_a2 ER -
%0 Journal Article %A A. I. Zenchuk %A S. V. Manakov %T The dual $\overline \partial$-problem, $(2+1)$-dimensional nonlinear evolution equations and their reductions %J Teoretičeskaâ i matematičeskaâ fizika %D 1995 %P 371-382 %V 105 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1995_105_3_a2/ %G ru %F TMF_1995_105_3_a2
A. I. Zenchuk; S. V. Manakov. The dual $\overline \partial$-problem, $(2+1)$-dimensional nonlinear evolution equations and their reductions. Teoretičeskaâ i matematičeskaâ fizika, Tome 105 (1995) no. 3, pp. 371-382. http://geodesic.mathdoc.fr/item/TMF_1995_105_3_a2/