Related papers: Generalized Bethe expansions of superconformal ind…
We derive formulas for the Reshetikhin-Turaev invariants of all oriented Seifert manifolds associated to an arbitrary complex finite dimensional simple Lie algebra $\mathfrak g$ in terms of the Seifert invariants and standard data for…
In this work we have developed the essential tools for the algebraic Bethe ansatz solution of integrable vertex models invariant by a unique U(1) charge symmetry. The formulation is valid for arbitrary statistical weights and respective…
We review aspects of superconformal indices in three dimension. Three dimensional superconformal indices can be exactly computed by using localization method including monopole contribution, and can be applied to provide evidences for…
There is a need for covariant solutions of bound state equations in order to construct realistic QCD based models of mesons and baryons. Furthermore, we ideally need to know the structure of these bound states in all kinematical regimes,…
We are looking for the universal covering algebra for all symmetries of a given pde, using the sine-Gordon equation as a typical example for a non-evolution equation. For non-evolution equations, Estabrook-Wahlquist prolongation structures…
Through a series of exact mappings we reinterpret the Bernoulli model of sequence alignment in terms of the discrete-time totally asymmetric exclusion process with backward sequential update and step function initial condition. Using…
We present an algebraic method for solving the Bethe ansatz equations for the periodic totally asymmetric exclusion process (TASEP) with an arbitrary number of sites and particles. The Bethe ansatz equations are realized as an algebraic…
We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe…
Uniform asymptotic expansions are derived for reverse generalised Bessel polynomials of large degree $n$, real parameter $a$, and complex argument $z$, which are simpler than previously known results. The defining differential equation is…
We study the supersymmetric extension of the gauged $ O(3) $ sigma model in $ 2+1 $ dimensions and find the supersymmetry algebra. We also discuss soliton solutions in case the Maxwell term is replaced by the Born-Infeld term. We show that…
We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficients. The generalisation is based on the method of Borel…
A detailed study of a model for strongly-interacting fermions with exclusion rules and lattice $\mathcal N=2$ supersymmetry is presented. A submanifold in the space of parameters of the model where it is Bethe-ansatz solvable is identified.…
We count the Bethe states of quantum integrable models with twisted boundary conditions using the Witten index of 2d supersymmetric gauge theories. For multi-component models solvable by the nested Bethe ansatz, the result is a novel…
We consider the Gelfand problem with rapidly growing nonlinearities in the two-dimensional bounded strictly convex domains. In this paper, we prove the uniformly boundedness of finite Morse index solutions. As a result, we show that there…
Whether integrable, partially integrable or nonintegrable, nonlinear partial differential equations (PDEs) can be handled from scratch with essentially the same toolbox, when one looks for analytic solutions in closed form. The basic tool…
This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…
We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference)…
I was asked to make my, by now quite old PhD thesis, available on the arxiv, for parts of it was never submitted for publication. The thesis offers a systematic study of stochastic differential equations (SDEs) on non-compact spaces. In…
We compute the eigenfunctions, energies and Bethe equations for a class of generalized integrable Hubbard models based on gl(n|m)\oplus gl(2) superalgebras. The Bethe equations appear to be similar to the Hubbard model ones, up to a phase…
This paper is devoted to the proof Gauss' divergence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently [2] and developed in [4], [5] and [6]. Their peculiarity is…