相关论文: On an integrable deformation of Kapustin-Witten sy…
Partly inspired by Sato's theory of the Kadomtsev-Petviashvili (KP) hierarchy, we start with a quite general hierarchy of linear ordinary differential equations in a space of matrices and derive from it a matrix Riccati hierarchy. The…
The aim of Part II is to explore the technique of invariance of tautological equations in the realm of Gromov--Witten theory. The main result is a proof of Invariance Theorem (Invariance Conjecture~1 in [14]), via the techniques from…
In this paper, as a step towards a unified mathematical treatment of the gauge functionals from quantum field theory that have found profound applications in mathematics, we generalize the Seiberg-Witten functional that in particular…
An initial-and boundary-value problem for the Kelvin-Voigt system, modeling a mixture of n incompressible and viscoelastic fluids, with non-constant density, is investigated in this work. The existence of global-in-time weak solutions is…
We present a method of constructing discrete integrable systems with crystallographic reflection group (Weyl) symmetries, thus clarifying the relationship between different discrete integrable systems in terms of their symmetry groups.…
We consider five-point differential-difference equations. Our aim is to find integrable modifications of the Ito-Narita-Bogoyavlensky equation related to it by non-invertible discrete transformations. We enumerate all modifications…
An elliptic analogue of the $q$ deformed Knizhnik-Zamolodchikov equations is introduced. A solution is given in the form of a Jackson-type integral of Bethe vectors of the XYZ-type spin chains.
We derive the Christoffel-Geronimus-Uvarov transformations of a system of bi-orthogonal polynomials and associated functions on the unit circle, that is to say the modification of the system corresponding to a rational modification of the…
In this note, we give an exposition of the construction of Seiberg-Witten invariants.
We consider dispersionless Lax systems and present a new systematic method of deriving new integrable systems from a given one. We provide examples that include: the dispersionless Hirota equation, the general heavenly equation and the web…
This paper describes an integrable Yang-Mills-Higgs system on (2+1)-dimensional de Sitter space-time. It is the curved-space-time analogue of the Bogomolnyi equations for monopoles on R^3. A number of solutions, of various types, are…
We briefly summarize our systematic construction procedure of q-deforming maps for Lie group covariant Weyl or Clifford algebras.
In this undergraduate thesis, we present an analytical proof of the Morse inequalities for closed smooth $n$-manifolds following Witten's approach. Using techniques from PDE theory, the proof is reduced to study the eigenspaces and…
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…
The Pavlov equation is one of the simplest integrable systems of vector fields arising from various problems of mathematical physics and differential geometry which are intensively studied in recent literature. In this report, solving a…
We study the integrability of the general two-dimensional Zakharov-Shabat systems, which appear in application of the inverse scattering transform (IST) to an important class of nonlinear partial differential equations (PDEs) called…
In this paper we classify all bounded travelling wave solutions for the integrable Dullin-Gottwald-Holm equation. It is shown that it decomposes in two known cases: the Camassa-Holm and the Korteweg-de Vries equation. For the former, the…
The Gromov-Witten theory of Deligne-Mumford stacks is a recent development, and hardly any computations have been done beyond 3-point genus 0 invariants. This paper provides explicit recursions which, together with some invariants computed…
The complete integrability of the hyperbolic Gaudin Hamiltonian and other related integrable systems is shown to be easily derived by taking into account their sl(2,R) coalgebra symmetry. By using the properties induced by such a coalgebra…
Using diffeomorphism group vector fields on $\mathbb{C}$-multiplied tori and the related Lie-algebraic structures, we study multi-dimensional dispersionless integrable systems that describe conformal structure generating equations of…