Related papers: A twisted integrable hierarchy with $\mathbb D_2$ …
An example of full solution of the inverse scattering problem on the half line is presented. For this purpose, a simple analytically solvable model system (Morse potential) is used, which is expected to be a reasonable approximation to a…
Integrable mixed models have been used as a generalization of traditional integrable models. However, a map from a traditional integrable model to a mixed integrable model is not well understood yet. Here, it is studied the relation between…
Twisted loop algebras of the second kind are infinite-dimensional Lie algebras that are constructed from a semisimple Lie algebra and an automorphism on it of order at most $2$. They are examples of equivariant map algebras. The…
We introduce a twisted quantum affine algebra associated to each simply laced finite dimensional simple Lie algebra. This new algebra is a Hopf algebra with a Drinfeld-type comultiplication. We obtain this algebra by considering its vertex…
The basic concepts underlying our analysis of {\it W-algebras} as extended symmetries of integrable systems are summarized. The construction starts from the second hamiltonian structure of ``Generalized Drinfel'd-Sokolov'' hierarchies, and…
A special case of the Fateev-Zamolodchikov model is studied resulting in a solution of the Yang-Baxter equation with two spectral parameters. Integrable models from this solution are shown to have the symmetry of the Drinfeld double of a…
The question of complete integrability of evolution equations associated to $n\times n$ first order isospectral operators is investigated using the inverse scattering method. It is shown that for $n>2$, e.g. for the three-wave interaction,…
In the example of the Schr\"odinger/KdV equation we give elementary treatment of the theory of finite-gap integration. The concept is equivalent to two kinds of Liouvillian integrability: quadrature integrability of linear differential…
Starting from some ideas given by Bales in [Ba; 09], in this paper we present an algorithm for computing the elements of the basis in an algebra obtained by the Cayley-Dickson process. As a consequence of this result, we prove that an…
We propose a new program for computing a certain integrand of scattering amplitudes of four-dimensional gauge theories which we call the \textit{form factor integrand}, starting from 6d holomorphic theories on twistor space. We show that…
We present the foundations of a new solution technique for the characteristic initial value problem (IVP) of colliding plane gravitational waves. It has extensive similarities to the approach of Alekseev and Griffiths in 2001, but we use an…
We realise the Shatashvili-Vafa superconformal algebra for $G_2$ string compactifications by combining Odake and free conformal algebras following closely the recent mathematical construction of twisted connected sum $G_2$ holonomy…
We propose a systematic treatment of symmetries of KP integrable systems, including constrained (reduced) KP models ${\sl cKP}_{R,M}$, and their multi-component (matrix) generalizations. Any such integrable hierarchy is shown to possess an…
We compute the Lie symmetry algebra of the generalized Davey-Stewartson (GDS) equations and show that under certain conditions imposed on parameters in the system it is infinite-dimensional and isomorphic to that of the standard integrable…
We explore the geometric interpretation of the twisted index of 3d ${\mathcal N} =4$ gauge theories on $S^1\times \Sigma$ where $\Sigma$ is a closed Riemann surface. We focus on a rich class of supersymmetric quiver gauge theories that have…
This paper develops the numerical inverse scattering transform (NIST) framework for the coupled modified Korteweg-de Vries (mKdV) equation based on its associated Riemann-Hilbert problem. The coupled system gives rise to a $3\times3$…
We construct a weight matrix for the 3D Ising model satisfying the so-called twisted tetrahedron equation. The result is based on the theory of the n-simplicial complex and the invented recursion procedure on the space of n-simplex…
We apply the technique of integrable extensions to the symmetry pseudo-group of the r-th mdKP equation. This gives another look on deriving known coverings and allows us to find new coverings for this equation.
We develop a ring-theoretic approach for blowing up many noncommutative projective surfaces. Let T be an elliptic algebra (meaning that, for some central element g of degree 1, T/gT is a twisted homogeneous coordinate ring of an elliptic…
The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is revisited from a novel point of view by showing that the quadratic Poisson structure underlying its integrability structure is just a real…