相关论文: Construction of Exact Solutions to Nahm's Equation…
We derive certain boundary conditions in Nahm's equations by considering a system of N parallel D1-branes perpendicular to a D3-brane in type IIB string theory.
We use the Nahm transform to construct explicit $L^2$ solutions to the Dirac equation in $\mathbb{R}^3$ in the background of one nonabelian $U(2)$ monopole with one positive and one negative Dirac singularity.
The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles. We show that the discrete Nahm equations are completely integrable in a natural…
The discrete Nahm equation is an integrable nonlinear difference equation for complex $N\times N$ matrices defined on a one-dimensional lattice, with rank and symmetry boundary conditions at the ends of the lattice. Solutions of this system…
We present explicit expressions for the fields of a charge one BPS monopole with two Dirac singularities. These are solutions of the nonlinear Bogomolny equations with the gauge group U(2) or SO(3). We derive these expressions by applying…
The Nahm pole boundary condition for certain gauge theory equations in four and five dimensions is defined by requiring that a solution should have a specified singularity along the boundary. In the present paper, we show that this boundary…
We classify all possible charge-3 monopole spectral curves with non-trivial automorphism group and within these identify those with elliptic quotients. By focussing on elliptic quotients the transcendental constraints for a monopole…
In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of vector and scalar generalized Hartmann potentials. This is done provided the vector potential is equal to or minus the scalar…
We treat the problem of completing the moduli space for roots of line bundles on curves. Special attention is devoted to higher spin curves within the universal Picard scheme. Two new different constructions, both using line bundles on…
In a multidimensional infinite layer bounded by two hyperplanes, the Poisson equation with the polynomial right-hand side is considered. It is shown that the Dirichlet boundary value problem and the mixed Dirichlet-Neumann boundary value…
We consider smooth solutions to the Monge-Amp`ere equation subject to mixed boundary conditions on annular domains. We establish global $C^2$ estimates when the boundary of the domain consists of two smooth strictly convex closed…
In a multidimensional infinite layer bounded by two hyperplanes, the inhomogeneous Helmholtz equation with a polynomial right-hand side is considered. It is shown that the Dirichlet and Dirichlet-Neumann boundary-value problems with…
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…
Representing vector fields by potentials can be a challenging task in domains with cavities or tunnels, due to the presence of harmonic fields which are both irrotational and solenoidal but may have no scalar or vector potentials. For…
Given an holomorphic Higgs bundle on a compact Riemann surface of genus greater than one, we construct a DQ-module supported by the spectral curve associated to this bundle. Then, we relate quantum curves arising in various situations…
We give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e. a smooth dynamical system on M whose positive semi-trajectories are…
I survey the theory of Bogomolny monopoles and the various approaches to their study. These include the spectral curve, Nahm correspondence and rational maps.
We consider Nahm's equations on a bounded open interval with first order poles at the ends. By imposing further boundary conditions, extended moduli spaces are identified with spaces of rational maps from $\mathbb{C}\mathrm{P}^1$ to…
Our approach to define monopoles is twistorial and we start by developing the twistor theory of R^5, which is an analogue of the twistor theory for R^3 developed by Hitchin. Using this, we describe a Hitchin-Ward transform for R^5, that…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…