This article is cited 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

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, 105:3, 1490–1499

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