Linearly degenerate hierarchies of quasiclassical SDYM type

Abstract

We demonstrate that SDYM equations for the Lie algebra of one-dimensional vector fields represent a natural reduction in the framework of general linearly degenerate dispersionless hierarchy. We define the reduction in terms of wave functions, introduce generating relation, Lax-Sato equations and the dressing scheme for the reduced hierarchy. Multidimensional case is also discussed.

21 pages; reference [10] and a comment after equation (7) added

References in corpus (1)

• Inverse Scattering Problem for Vector Fields and the Cauchy Problem for the Heavenly Equation

Cited by in corpus (4)

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