Related papers: Two new multi-component BKP hierarchies
A $\bar{\partial}$-formalism for studying dispersionless integrable hierarchies is applied to the dKP hierarchy. Connections with the theory of quasiconformal mappings on the plane are described and some clases of explicit solutions of the…
This paper is devoted to the problem of the description of nonequilibrium correlations in quantum many-particle systems. The nonlinear quantum BBGKY hierarchy for marginal correlation operators is rigorously derived from the von Neumann…
We obtain new BPS solutions of six-dimensional, N = 1 supergravity coupled to a tensor multiplet. These solutions are sourced by multiple "superthreads" carrying D1-D5-P charges and two magnetic dipole charges. These new solutions are…
Bilevel optimization involves a hierarchical structure where one problem is nested within another, leading to complex interdependencies between levels. We propose a single-loop, tuning-free algorithm that guarantees anytime feasibility,…
Nonlinear integrable equations, such as the KdV equation, the Boussinesq equation and the KP equation, have the close relation with many-body problem. The solutions of such equations are the same as the restricted flows of the classical…
We uncover a precise relation between superblocks for correlators of superconformal field theories (SCFTs) in various dimensions and symmetric functions related to the $BC$ root system. The theories we consider are defined by two integers…
We introduce an S-function formulation for the recently found r-th dispersionless modified KP and r-th dispersionless Dym hierarchies, giving also a connection of these $S$-functions with the Orlov functions of the hierarchies. Then, we…
Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own…
Starting from free charged fermions we give equivalent definitions of the $n\/$-component KP hierarchy, in terms of $\tau\/$-functions $\tau_\alpha\/$ (where $\alpha \in M =\/$ root lattice of $sl_n\/$), in terms of $n \times n\/$ matrix…
We investigate a stability equation involving two-component eigenfunctions which is associated with a potential model in terms of two coupled real scalar fields, which presents non BPS topological defect.
We show that the local Burkholder functional $\mathcal B_K$ is quasiconvex. In the limit of $p$ going to 2 we find a class of non-polyconvex functionals which are quasiconvex on the set of matrices with positive determinant. In order to…
In this paper, we propose a two-level block preconditioned Jacobi-Davidson (BPJD) method for efficiently solving discrete eigenvalue problems resulting from finite element approximations of $2m$th ($m = 1, 2$) order symmetric elliptic…
We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the…
We study Manakov-Santini equation, starting from Lax-Sato form of associated hierarchy. The waterbag reduction for Manakov-Santini hierarchy is introduced. Equations of reduced hierarchy are derived.We construct new coordinates transforming…
Analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is discussed. It is based on the generalized Hirota identity. This approach allows to represent generalized hierarchies of…
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…
In this paper, we propose two iterative methods for finding a common solution of a finite family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid extragradient-cutting algorithm which is extended from…
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 we study a class of unconstrained and constrained bilevel optimization problems in which the lower level is a possibly nonsmooth convex optimization problem, while the upper level is a possibly nonconvex optimization problem.…
A new (1+1)-dimensional integrable system, i. e. the super coupled Korteweg-de Vries (cKdV) system, has been constructed by a super extension of the well-known (1+1)-dimensional cKdV system. For this new system, a novel symmetry constraint…