Related papers: Solution to SU(n+1) Toda system generated by spher…
: We consider two--dimensional supersymmetric Toda theories based on the Lie superalgebras $A(n,n)$, $D(n+1,n)$ and $B(n,n)$ which admit a fermionic set of simple roots and a fermionic untwisted affine extension. In particular, we…
We prove that in conformal classes of metrics near the class of an Einstein metric (other than the standard round metric on a sphere) the Yamabe problem has a unique solution up to scaling. This is a local extension, in the space of…
The multidimensional gravity on the principal bundle with the SU(2) gauge group is considered. The numerical investigation of the spherically symmetric metrics with the center of symmetry is made. The solution of the gravitational equations…
We are solving the classical Riemann-Hilbert problem of rank N>1 on the extended complex plane punctured in 2m+2 points, for NxN quasi-permutation monodromy matrices. Following Korotkin we solve the Riemann-Hilbert problem in terms of the…
Spherically symmetric solutions of the SU(N) Einstein-Yang-Mills-Higgs system are constructed using the harmonic map ansatz. The problem reduces to solving a set of ordinary differential equations for the appropriate profile functions. In…
We show how to lift solutions of Euclidean Einstein-Maxwell equations with non-zero cosmological constant to solutions of eleven-dimensional supergravity theory with non-zero fluxes. This yields a class of 11D metrics given in terms of…
In Part I (arXiv:1209.2045) we computed the Stokes data, though not the "connection matrix", for the smooth solutions of the tt*-Toda equations whose existence we established by p.d.e. methods. Here we give an alternative proof of the…
We examine the relation between two known classes of solutions of the sine--Gordon equation, which are expressed by theta functions on hyperelliptic Riemann surfaces. The first one is a consequence of the Fay's trisecant identity. The…
We investigate the geometry of a certain space of meromorphic connections with irregular singularities, and prove in particular that it is a (real) symplectic Lie groupoid. The connections have a physical meaning: they correspond to certain…
In this paper we consider the so-called Toda system of equations on a compact surface. In particular, we discuss the parity of the Leray-Schauder degree of that problem. Our main tool is a theorem of Krasnoselskii and Zabreiko on the degree…
Manifest N=2 supersymmetric Toda systems are constructed from the $sl(n,n+1)$ superalgebras by taking into account their complex structure. In the $n\to \infty$ continuum limit an N=2 extension of the $(2+1)$-dimensional heavenly equation…
We consider the iso-spectral real manifolds of tridiagonal Hessenberg matrices with real eigenvalues. The manifolds are described by the iso-spectral flows of indefinite Toda lattice equations introduced by the authors [Physica, 91D (1996),…
Gorsky et al. presented an explicit construction of Whitham deformations of the Seiberg-Witten curve for the $SU(N+1)$ $\calN = 2$ SUSY Yang-Mills theory. We extend their result to all classical gauge groups and some other cases such as the…
We consider the existence problem of the following Singular Toda system on a compact Riemann surface $(\Sigma, g)$ without boundary \begin{equation*} \begin{cases}…
Geometry of holomorphic curves from point of view of open Toda systems is discussed. Parametrization of curves related this way to non-exceptional simple Lie algebras is given. This gives rise to explicit formulas for minimal surfaces in…
We study some static multi-soliton configurations in the su(N + 1) Toda models. Such configurations exist for N > 1. We construct explicitly a multi-soliton solution for any N and study conditions for having such solutions. The number of…
In this article we obtain total masses of solutions to the Toda system associated to a general simple Lie algebra with singular sources at the origin. The determination of such total masses is one of the important steps towards establishing…
The hierarchy of the classical nonlinear integrable equations associated with relativistic Toda chain model is considered. It is formulated for the N-th powers of the quantum operators of the corresponding quantum integrable models.…
All spherically symmetric Riemannian metrics of constant scalar curvature in any dimension can be written down in a simple form using areal coordinates. All spherical metrics are conformally flat, so we search for the conformally flat…
We find an infinite class of non-supersymmetric multi-center solutions to the STU model in five-dimensional ungauged supergravity coupled to two vector multiplets. The solutions are obtained by solving a system of linear equations on a…