Related papers: Dispersionless DKP hierarchy and elliptic Lowner e…
We show that the dispersionless limits of the Pfaff-KP (also known as the DKP or Pfaff lattice) and the Pfaff-Toda hierarchies admit a reformulation through elliptic functions. In the elliptic form they look like natural elliptic…
We consider multi-variable reductions of the dispersionless DKP hierarchy (the dispersionless limit of the Pfaff lattice) in the elliptic parametrization. The reduction is given by a system of elliptic L\"owner equations supplemented by a…
We consider the dispersionless limit of the recently introduced multi-component Pfaff-Toda hierarchy. Its dispersionless version is a set of nonlinear differential equations for the dispersionless limit of logarithm of the tau-function (the…
We show that one-variable reductions of the Pfaff-Toda integrable hierarchy in the dispersionless limit are described by a system of coupled elliptic L\"owner (Komatu-Goluzin) equations.
Reduction of a dispersionless type integrable system (dcmKP hierarchy) to the radial Loewner equation is presented.
Recently the study of Fay-type identities revealed some new features of the DKP hierarchy (also known as "the coupled KP hierarchy" and "the Pfaff lattice"). Those results are now extended to a Toda version of the DKP hierarchy (tentatively…
Using the free fermions technique and bosonization rules we introduce the multicomponent DKP hierarchy as a generating bilinear integral equation for the tau-function. A number of bilinear equations of the Hirota-Miwa type are obtained as…
We exhibit the dispersionless limit of the extended discrete KP hierarchy.
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…
We define the coupled modified KP hierarchy and its dispersionless limit. This integrable hierarchy is a generalization of the ''half'' of the Toda lattice hierarchy as well as an extension of the mKP hierarchy. The solutions are…
The dispersionless limit of the scalar nonlocal dbar-problem is derived. It is given by a special class of nonlinear first-order equations. A quasi-classical version of the dbar-dressing method is presented. It is shown that the algebraic…
It has been shown that the dispersionless KP hierarchy (or the Benney hierarchy) is reduced to the chordal L\"owner equation. We show that the radial L\"owner equation also gives reduction of a dispersionless type integrable system. The…
The equations of Loewner type can be derived in two very different contexts: one of them is complex analysis and the theory of parametric conformal maps and the other one is the theory of integrable systems. In this paper we compare the…
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 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…
We show that $N$-variable reduction of the dispersionless BKP hierarchy is described by a L\"owner type equation for the quadrant.
We define and study dispersionless coupled modified KP hierarchy, which incorporates two different versions of dispersionless modified KP hierarchies.
We revisit dispersionless version of the multicomponent KP hierarchy considered previously by Takasaki and Takebe. In contrast to their study, we do not fix any distinguished component treating all of them on equal footing. We obtain…
The Loewner equation is known as a one-dimensional reduction of the Benney chain as well as the dispersionless KP hierarchy. We propose a reverse process showing that time splitting in the Loewner or the Loewner-Kufarev equation leads to…
We investigate self-similar solutions of the extended discrete KP hierarchy. It is shown that corresponding ansatzes lead to purely discrete equations with dependence on some number of parameters together with equations governing…