Related papers: A new extended matrix KP hierarchy and its solutio…
We obtain the bi-Hamiltonian structure of the super KP hierarchy based on the even super KP operator $\Lambda = \theta^{2} + \sum^{\infty}_{i=-2}U_{i} \theta^{-i-1}$, as a supersymmetric extension of the ordinary KP bi-Hamiltonian…
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…
Based on the Lax operator $L$ and Orlov-Shulman's $M$ operator, the string equations of the $q$-KP hierarchy are established from special additional symmetry flows, and the negative Virasoro constraint generators \{$L_{-n}, n\geq1$\} of the…
A KP-mKP hierarchy was introduced recently via pseudo-differential operators containing two derivations. In this paper, for the KP-mKP hierarchy we derive a class of (differential) Fay identities and construct a series of additional…
We derive some rational solutions for the multicomponent and matrix KP hierarchies generalising an approach by Wilson. Connections with the multicomponent version of the KP/CM correspondence are discussed.
Matrix hierarchies are: multi-component KP, general Zakharov-Shabat (ZS) and its special cases, e.g., AKNS. The ZS comprises all integrable systems having a form of zero-curvature equations with rational dependence of matrices on a spectral…
We consider trigonometric solutions of the KP hierarchy. It is known that their poles move as particles of the Calogero-Moser model with trigonometric potential. We show that this correspondence can be extended to the level of hierarchies:…
We study the conformal properties of the multi-constraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extension of $W_n$…
The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the 't Hooft expansion for matrix integral, these solutions are described by…
Using the determinant representation of gauge transformation operator, we have shown that the general form of $\tau$ function of the $q$-KP hierarchy is a q-deformed generalized Wronskian, which includes the q-deformed Wronskian as a…
The hierarchy structure associated with a (2+1)-dimensional Nonlinear Schroedinger equation is discussed as an extension of the theory of the KP hierarchy. Several methods to construct special solutions are given. The relation between the…
The multicomponent 2D Toda hierarchy is analyzed through a factorization problem associated to an infinite-dimensional group. A new set of discrete flows is considered and the corresponding Lax and Zakharov--Shabat equations are…
In this paper, the compatibility between the integral type gauge transformation and the additional symmetry of the constrained KP hierarchy is given. And the string-equation constraint in matrix models is also derived.
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…
As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a novel space-time coupled algorithm for solving an inverse problem…
We construct a broad class of solutions of the KP-I equation by using a reduced version of the Grammian form of the $\tau$-function. The basic solution is a linear periodic chain of lumps propagating with distinct group and wave velocities.…
A wave function of the $N$-component KP Hierarchy with continuous flows determined by an invertible matrix $H$ is constructed from the choice of an $MN$-dimensional space of finitely-supported vector distributions. This wave function is…
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…
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…
A coupled AKNS-Kaup-Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and tri-Hamiltonian structures are established for…