Quasi-classical $\dbar$-method: Generating equations for dispersionless integrable hierarchies

Abstract

The quasi-classical $\bar{\partial }$-dressing method is used to derive compact generating equations for dispersionless hierarchies. Dispersionless Kadomtsev-Petviashvili (KP) and two-dimensional Toda lattice (2DTL) hierarchies are considered as illustrative examples.

11 pages, the text of the talk at NEEDS 2001 conference

Cited by in corpus (5)

• The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type
• From AKNS to derivative NLS hierarchies via deformations of associative products
• Second order quasilinear PDEs and conformal structures in projective space
• Quasi-classical DBAR-dressing approach to the weakly dispersive KP hierarchy
• On a class of three-dimensional integrable Lagrangians