Related papers: Two dimensional KP systems and their solvability
Following Natanzon-Zabrodin, we explore the Kadomtsev-Petviashvili hierarchy as an infinite system of mutually consistent relations on the second derivatives of the free energy with some universal coefficients. From this point of view,…
We review the integration of the KP hierarchy in several non-standard contexts. Specifically, we consider KP in the following associative differential algebras: an algebra equipped with a nilpotent derivation; an algebra of functions…
We recall the notions of Fr\"olicher and diffeological spaces and we build regular Fr\"olicher Lie groups and Lie algebras of formal pseudo-differential operators in one independent variable. Combining these constructions with a smooth…
The review is devoted to the integrable properties of the Generalized Kontsevich Model which is supposed to be an universal matrix model to describe the conformal field theories with $c<1$. It is shown that the deformations of the…
Partly inspired by Sato's theory of the Kadomtsev-Petviashvili (KP) hierarchy, we start with a quite general hierarchy of linear ordinary differential equations in a space of matrices and derive from it a matrix Riccati hierarchy. The…
We classify the Lie point symmetries for the 2+1 nonlinear generalized Kadomtsev-Petviashvili equation by determine all the possible f(u) functional forms where the latter depends. For each case the one-dimensional optimal system is…
We present (2+1)-dimensional generalizations of the k-constrained Kadomtsev-Petviashvili (k-cKP) hierarchy and corresponding matrix Lax representations that consist of two integro-differential operators. Additional reductions imposed on the…
We derive a particular solution of the extended $r$-reduced KP hierarchy, which is specified by a generalized string equation. The work is a generalization to arbitrary $r\geq 2$ of Buryak's recent results of a solution to the extended open…
Following the techniques of M. Sato (see \cite{Sa}), a generalization of the KP hierarchy for more than one variable is proposed. An approach to the classification of solutions and a method to construct algebraic solutions is also offered.
We study a Kadomtsev-Petviashvili system for the local Camassa-Holm hierarchy obtaining a candidate to the Baker-Akhiezer function for its first reduction generalizing the local Camassa-Holm. We focus our attention on the differences with…
In this paper, we investigate the non-autonomous discrete Kadomtsev-Petviashvili (KP) system in terms of generalized Cauchy matrix approach. These equations include non-autonomous bilinear lattice KP equation, non-autonomous lattice…
The KP hierarchy is a completely integrable system of quadratic, partial differential equations that generalizes the KdV hierarchy. A linear combination of Schur functions is a solution to the KP hierarchy if and only if its coefficients…
By using pseudo-differential operators containing two derivations, we extend the Kadomtsev-Petviashvili (KP) hierarchy to a certain KP-mKP hierarchy. For the KP-mKP hierarchy, we obtain its B\"{a}cklund transformations, bilinear equations…
In this note we consider a two-component extension of the Kadomtsev-Petviashvili (KP) hierarchy represented with two types of pseudo-differential operators, and construct its Hamiltonian structures by using the $R$-matrix formalism.
We extend Gesztesy-Holden's method to 2+1 dimensional case to obtain a unified construction to the algebro-geometric solutions of the whole modified Kadomtsev-Petviashvili (mKP) hierarchy. Our tools include the relations between solutions…
An extension of the Kadomtsev-Petviashvili (KP) hierarchy defined via scalar pseudo-differential operators was studied in [16, 20]. In this paper, we represent the extended KP hierarchy into the form of bilinear equation of (adjoint)…
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.
A characterization of the Kadomtsev-Petviashvili hierarchy of type C (CKP) in terms of the KP tau-function is given. Namely, we prove that the CKP hierarchy can be identified with the restriction of odd times flows of the KP hierarchy on…
In this paper, we investigate the $(k, m)$-constrained 1st modified Kadomtsev-Petviashvili (mKP) hierarchy $(L^k)_{\leq 0}= \sum_{i=1}^m q_i \partial^{-1} r_i \partial$. Here, we obtain the corresponding solutions in the form of generalized…
We describe three different approaches to the extended (N=2) supersymmetrization of the multicomponent KP hierarchy. In the first one we utilize only superfermions while in the second only superbosons and in the third superbosons as well as…