Theoretical and Mathematical Physics

, Volume 105, Issue 3, pp 1490–1499 | Cite as

Dual 1490-11490-11490-1-problem, (2+1)-dimensional intergrable nonlinear evolution equations and their reductions

  • A. I. Zenchuk
  • S. V. Manakov


For a compact description of integrable systems of partial derivative equations (PDE), with singular dispersion relations in (2+1)-dimensions, the dual\(\bar \partial \)-problem with arbitrary normalization is used. Symmetry reductions and the corresponding Lax representations are discussed. The singular KP-hierarchy, as well as the Schrödinger equation with a magnetic field, are considered as examples.


Magnetic Field Dispersion Relation Evolution Equation Integrable System Nonlinear Evolution 
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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • A. I. Zenchuk
    • 1
  • S. V. Manakov
    • 1
  1. 1.Landau Institute for Theoretical PhysicsUSSR

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