Related papers: Extended discrete KP hierarchy and its dispersionl…
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 introduce a general setting for multidimensional dispersionless integrable hierarchy in terms of differential $m$-form $\Omega_m$ with the coefficients satisfying the Pl\"ucker relations, which is gauge-invariantly closed and its…
In this short note, we address the discretization of optimal control problems with higher order polynomials. We develop a necessary and sufficient condition to ensure that weak limits of discrete feasible controls are feasible for the…
We develop the notion of discrete degrees of freedom of a log-concave sequence and use it to prove that geometric distribution minimises R\'enyi entropy of order infinity under fixed variance, among all discrete log-concave random variables…
In the recent paper [Stud. App. Math. 147 (2021) 752], squared eigenfunction symmetry constraint of the differential-difference modified Kadomtsev-Petviashvili (D$\Delta$mKP) hierarchy converts the D$\Delta$mKP system to the relativistic…
In this note we discuss the nature of gaps in the support of a discretely infinitely divisible distribution from the angle of compound Poisson laws/processes. The discussion is extended to infinitely divisible distributions on the…
In this paper, we consider the dispersive limit of the Euler-Poisson system for ion-acoustic waves. We establish that under the Gardner-Morikawa type transformations, the solutions of the Euler-Poisson system converge globally to the…
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…
We present recent developments on geometric theory of the Hirota system and of the non-commutative discrete Kadomtsev-Petviashvili (KP) hierarchy adding also some new results which make the picture more complete. We pay special attention to…
We study a new flexible method to extend linearly the graph of a non-linear, and usually not bijective, function so that the resulting extension is a bijection. Our motivation comes from cryptography. Examples from symmetric cryptography…
The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end we first study…
We investigate the additional symmetries of several supersymmetric KP hierarchies: the SKP hierarchy of Manin and Radul, the $\hbox{SKP}_2$ hierarchy, and the Jacobian SKP hierarchy. In all three cases we find that the algebra of symmetries…
We study discrete complex analysis and potential theory on a large family of planar graphs, the so-called isoradial ones. Along with discrete analogues of several classical results, we prove uniform convergence of discrete harmonic…
In these notes, the Christoffel-Darboux polynomial kernel is extended to infinite-dimensional Hilbert spaces, following as closely as possible its original finite-dimensional treatment.
In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…
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…
Given an arbitrary measurable cardinal $\kappa$, a nondiscrete Hausdorff extremally disconnected topological group of cardinality $\kappa$ is constructed.
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…
We establish the existence of real pole-free solutions to all even members of the Painlev\'e I hierarchy. We also obtain asymptotics for those solutions and describe their relevance in the description of critical asymptotic behavior of…