Related papers: Coupled Modified KP Hierarchy and Its Dispersionle…
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…
There are well-known constructions of integrable systems which are chains of infinitely many copies of the equations of the KP hierarchy ``glued'' together with some additional variables, e.g., the modified KP hierarchy. Another…
For a family of Poisson algebras, parametrized by by an integer number r, and an associated Lie algebraic splitting, we consider the factorization of given canonical transformations. In this context we rederive the recently found r-th…
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…
The B\"{a}cklund transformations between the constrained dispersionless KP hierarchy (cdKPH) and the constrained dispersionless mKP hieararchy (cdmKPH) and between the dispersionless KP hieararchy with self-consistent sources (dKPHSCS) and…
We first show that the quasiclassical limit of the squared eigenfunction symmetry constraint of the Sato operator for the mKP hierarchy leads to a reduction of the Sato function for the dispersionless mKP hierarchy. The constrained…
We investigate the Miura map between the dispersionless KP and dispersionless modified KP hierarchies. We show that the Miura map is canonical with respect to their bi-Hamiltonian structures. Moreover, inspired by the works of Takasaki and…
We review the notion of differential Fay identities and demonstrate, through case studies, its new role in integrable hierarchies of the KP type. These identities are known to be a convenient tool for deriving dispersionless Hirota…
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…
In this paper, modified Toda (mToda) equation is generalized to form an integrable hierarchy in the framework of Sato theory, which is therefore called mToda hierarchy. Inspired by the fact that Toda hierarchy is 2-component generalization…
Additional non-isospectral symmetries are formulated for the constrained Kadomtsev-Petviashvili (\cKP) integrable hierarchies. The problem of compatibility of additional symmetries with the underlying constraints is solved explicitly for…
In this paper, we construct the multicomponent modified KP hierarchy and its additional symmetries. The additional symmetries constitute an interesting multi-folds quantum torus type Lie algebra. By a reduction, we also construct the…
We prove the dispersionless Hirota equations for the dispersionless Toda, dispersionless coupled modified KP and dispersionless KP hierarchies using an idea from classical complex analysis. We also prove that the Hirota equations…
Reduction of a dispersionless type integrable system (dcmKP hierarchy) to the radial Loewner equation is presented.
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 introduce the discrete hierarchy which naturally generalizes well known discrete KP hierarchy.
The constrained Modified KP hierarchy is considered from the viewpoint of modification. It is shown that its second Poisson bracket, which has a rather complicated form, is associated to a vastly simpler bracket via Miura-type map. The…
Some new developments in constrained Lax integrable systems and their applications to physics are reviewed. After summarizing the tau function construction of the KP hierarchy and the basic concepts of the symmetry of nonlinear equations,…
A new infinite set of commuting additional (``ghost'') symmetries is proposed for the KP-type integrable hierarchy. These symmetries allow for a Lax representation in which they are realized as standard isospectral flows. This gives rise to…
We propose one possible generalization of the KP hierarchy, which possesses multi bi--hamiltonian structures, and can be viewed as several KP hierarchies coupled together.