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SU(4) Einstein-Yang-Mills theory possesses sequences of static spherically symmetric globally regular and black hole solutions. Considering solutions with a purely magnetic gauge field, based on the 4-dimensional embedding of $su(2)$ in…

We propose a set of conventional Bethe Ansatz equations and a corresponding expression for the eigenvalues of the transfer matrix for the open spin-1/2 XXZ quantum spin chain with nondiagonal boundary terms, provided that the boundary…

We consider a general class of boundary terms of the open XYZ spin-1/2 chain compatible with integrability. We have obtained the general elliptic solution of $K$-matrix obeying the boundary Yang-Baxter equation using the $R$-matrix of the…

We study the image of $\textrm{SU}(n)$ under the diagonal product map. Using only elementary tools of linear algebra, analysis and general topology, we find the analytical formula for the boundary of this image and find all special unitary…

We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…

In this article, we extend the work of arXiv:0901.4744 to a Bethe/Gauge correspondence between 2d (or resp. 3d) SO/Sp gauge theories and open XXX (resp. XXZ) spin chains with diagonal boundary conditions. The case of linear quiver gauge…

In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.

In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz…

The spectrum and partition function of a model consisting of SU(n) spins positioned at the equilibrium positions of a classical Calogero model and interacting through inverse-square exchange are derived. The energy levels are equidistant…

We study the homogenization problem of semi linear reflected partial differential equations (reflected PDEs for short) with nonlinear Neumann conditions. The non-linear term is a function of the solution but not of its gradient. The proof…

We formulate a notion of abstract loop equations, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The Schwinger-Dyson equation of the one and two…

We consider the focusing wave equation outside a ball of $\R^3$, with Dirichlet boundary condition and a superquintic power nonlinearity. We classify all radial stationary solutions, and prove that all radial global solutions are…

We present a new approach to Hamilton's theory of turns for the groups SO(3) and SU(2) which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire…

We use the Dunkl operator approach to construct one dimensional integrable models describing N particles with internal degrees of freedom. These models are described by a general Hamiltonian belonging to the center of the Yangian or the…

We develop the effective non-Hermitian Hamiltonian approach for open systems with Neumann boundary conditions. The approach can be used for calculating the scattering matrix and the scattering function in open resonator-waveguide systems.…

We construct regular and black hole solutions in SU(2) Einstein-Born-Infeld theory. These solutions have many features in common with the corresponding SU(2) Einstein-Yang-Mills solutions. In particular, sequences of neutral non-abelian…

We consider the Hamiltonian of the closed $SU(2)_{q}$ invariant chain. We project a particular class of statistical models belonging to the unitary minimal series. A particular model corresponds to a particular value of the coupling…

We prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed point index. Some of the…

An orthogonal basis of the Hilbert space for the quantum spin chain associated with the su(3) algebra is introduced. Such kind of basis could be treated as a nested generalization of separation of variables (SoV) basis for high-rank quantum…

We present the classification of the most general regular solutions to the boundary Yang-Baxter equations for vertex models associated with non-exceptional affine Lie algebras. Reduced solutions found by applying a limit procedure to the…