Quasi-classical DBAR-dressing approach to the weakly dispersive KP hierarchy
arXiv:nlin/0303063 · doi:10.1088/0305-4470/36/47/010
Abstract
Recently proposed quasi-classical DBAR-dressing method provides a systematic approach to study the weakly dispersive limit of integrable systems. We apply the quasi-classical DBAR-dressing method to describe dispersive corrections of any order. We show how calculate the DBAR problems at any order for a rather general class of integrable systems, presenting explicit results for the KP hierarchy case. We demonstrate the stability of the method at each order. We construct an infinite set of commuting flows at first order which allow a description analogous to the zero order (purely dispersionless) case, highlighting a Whitham type structure. Obstacles for the construction of the higher order dispersive corrections are also discussed.
arXiv comment24 pages
References in corpus (17)
- 2D Gravity and Random Matrices
- Integrability and Matrix Models
- Integrable Structure of Interface Dynamics
- Conformal maps and dispersionless integrable hierarchies
- Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation
- Integrable Structure of the Dirichlet Boundary Problem in Two Dimensions
- SDiff(2) KP hierarchy
- Solution of the dispersionless Hirota equations
- Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy
- On Associativity Equations in Dispersionless Integrable Hierarchies
- Dispersionless scalar integrable hierarchies, Whitham hierarchy and the quasi-classical dbar-dressing method
- Deformations of bihamiltonian structures of hydrodynamic type
- Singular sector of the Burgers-Hopf hierarchy and deformations of hyperelliptic curves
- dbar-equations, integrable deformations of quasiconformal mappings and Whitham hierarchy
- Integrable Structures in String Field Theory
- Generating Functional in CFT and Effective Action for Two-Dimensional Quantum Gravity on Higher Genus Riemann Surfaces
- Quasi-classical $\dbar$-method: Generating equations for dispersionless integrable hierarchies