相关论文: dbar-approach to the dispersionless KP hierarchy
The quasi-classical limit of the scalar nonlocal dbar-problem is derived and a quasi-classical version of the dbar-dressing method is presented. Dispersionless KP, mKP and 2DTL hierarchies are discussed as illustrative examples. It is shown…
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…
It is shown that the dispersionless scalar integrable hierarchies and, in general, the universal Whitham hierarchy are nothing but classes of integrable deformations of quasiconformal mappings on the plane. Examples of deformations of…
It is proved that the action for nonlinear Beltrami equation (quasiclassical dbar-problem) evaluated on its solution gives a tau-function for dispersionless KP hierarchy. Infinitesimal transformations of tau-function corresponding to…
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…
A $\bar{\partial}$-formalism for studying dispersionless integrable hierarchies is applied to the dKP hierarchy. Connections with the theory of quasiconformal mappings on the plane are described and some clases of explicit solutions of the…
The dispersionless KP hierarchy is considered from the point of view of the twistor formalism. A set of explicit additional symmetries is characterized and its action on the solutions of the twistor equations is studied. A method for…
The usual dispersionless limit of the KP hierarchy does not work in the case where the dependent variable has values in a noncommutative (e.g. matrix) algebra. Passing over to the potential KP hierarchy, there is a corresponding scaling…
The dispersionless KP and Toda hierarchies possess an underlying twistorial structure. A twistorial approach is partly implemented by the method of Riemann-Hilbert problem. This is however still short of clarifying geometric ingredients of…
Integrable dispersionless Kadomtsev-Petviashvili (KP) hierarchy of B type is considered. Addition formula for the $\tau$-function and conformally invariant equations for the dispersionless BKP (dBKP) hierarchy are derived. Symmetry…
Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced as a canonical transformation, quantization of which is…
For the first time we show that the quasiclassical limit of the symmetry constraint of the KP hierarchy leads to the generalized Zakharov reduction of the dispersionless KP (dKP) hierarchy which has been proved to be result of symmetry…
The factorization problem of the multi-component 2D Toda hierarchy is used to analyze the dispersionless limit of this hierarchy. A dispersive version of the Whitham hierarchy defined in terms of scalar Lax and Orlov--Schulman operators is…
We discuss the origin of the associativity (WDVV) equations in the context of quasiclassical or Whitham hierarchies. The associativity equations are shown to be encoded in the dispersionless limit of the Hirota equations for KP and Toda…
Reduction of a dispersionless type integrable system (dcmKP hierarchy) to the radial Loewner equation is presented.
Integrable hierarchies associated with the singular sector of the KP hierarchy, or equivalently, with $\dbar$-operators of non-zero index are studied. They arise as the restriction of the standard KP hierarchy to submanifols of finite…
We exhibit the dispersionless limit of the extended discrete KP hierarchy.
We show that the dispersionless DKP hierarchy (the dispersionless limit of the Pfaff lattice) admits a suggestive reformulation through elliptic functions. We also consider one-variable reductions of the dispersionless DKP hierarchy and…
A class of nonlinear problems on the plane, described by nonlinear inhomogeneous $\bar{\partial}$-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources) is described…
The BKP hierarchy has a two-component analogue (the 2-BKP hierarchy). Dispersionless limit of this multi-component hierarchy is considered on the level of the $\tau$-function. The so called dispersionless Hirota equations are obtained from…