Related papers: A new extended matrix KP hierarchy and its solutio…
Lattices of polynomial KP and BKP $\tau$-functions labelled by partitions, with the flow variables equated to finite power sums, as well as associated multipair KP and multipoint BKP correlation functions are expressed via generalizations…
We illustrate the basic notions of {\em additional non-isospectral symmetries} and their interplay with the discrete {\em \DB transformations} of integrable systems at the instance of {\em constrained Kadomtsev-Petviashvili} (\cKP)…
We find all formal solutions to the $\hbar$-dependent KP hierarchy. They are characterized by certain Cauchy-like data. The solutions are found in the form of formal series for the tau-function of the hierarchy and for its logarithm (the…
Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some…
Reductions of the KP-Whitham system, namely the (2+1)-dimensional hydrodynamic system of five equations that describes the slow modulations of periodic solutions of the Kadomtsev-Petviashvili (KP) equation, are studied. Specifically, the…
A method for introducing the higher order terms in the potential expansion to study the continuous limits of the Toda hierarchy is proposed in this paper. The method ensures that the higher order terms are differential polynomials of the…
The fully discrete problem for convection-diffusion equation is considered. It comprises compact approximations for spatial discretization, and Crank-Nicolson scheme for temporal discretization. The expressions for the entries of inverse of…
For each partition p of an integer N \geq 2, consisting of r parts, an integrable hierarchy of Lax type Hamiltonian PDE has been constructed recently by some of us. In the present paper we show that any tau-function of the p-reduced…
Invariant submanifolds of the so-called Darboux-KP chain are investigated. It is shown that restriction of dynamics on some class of invariant submanifolds yields the extension of the discrete KP hierarchy, while the intersections leads to…
A higher dimensional analogue of the KP hierarchy is presented. Fundamental constituents of the theory are pseudo-differential operators with Moyal algebraic coefficients. The new hierarchy can be interpreted as large-$N$ limit of…
We consistently develop a recently proposed scheme of matrix extension of dispersionless integrable systems for the general case of multidimensional hierarchies, concentrating on the case of dimension $d\geqslant 4$. We present extended Lax…
In this paper, we construct the quantum Torus symmetry of the KP hierarchy and further derive the quantum torus constraint on the tau function of the KP hierarchy. That means we give a nice representation of the quantum Torus Lie algebra in…
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…
Non-holonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the so-called "squared solutions" (squared eigenfunctions). Such deformations are equivalent to perturbed models with external…
Complete eigenfunctions of linearized integrable equations expanded around an arbitrary solution are obtained for the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and the Korteweg-de Vries (KdV) hierarchy. It is shown that the linearization…
The partition function for unitary two matrix models is known to be a double KP tau-function, as well as providing solutions to the two dimensional Toda hierarchy. It is shown how it may also be viewed as a Borel sum regularization of…
We present a theory of 'maximal' super-KP(SKP) hierarchy whose flows are maximally extended to include all those of known SKP hierarchies, including, for example, the MRSKP hierarchy of Manin and Radul and the Jacobian SKP(JSKP) introduced…
We develop a formalism of multicomponent BKP hierarchies using elementary geometry of spinors. The multicomponent KP and the modified KP hierarchy (hence all their reductions like KdV, NLS, AKNS or DS) are reductions of the multicomponent…
In practice, non-specialized interior point algorithms often cannot utilize the massively parallel compute resources offered by modern many- and multi-core compute platforms. However, efficient distributed solution techniques are required,…
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.