Related papers: A twisted integrable hierarchy with $\mathbb D_2$ …
In this paper, we discuss an interaction between complex geometry and integrable systems. Section 1 reviews the classical results on integrable systems. New examples of integrable systems, which have been discovered, are based on the Lax…
In this paper we present an overview of the connection between completely integrable systems and the background geometry of the flow. This relation is better seen when using a group-based concept of moving frame introduced by Fels and Olver…
We investigate static cylindrical solutions within an extended theory of modified gravity. By incorporating various coupling functions through a straightforward boost symmetry approach, we establish the equations of motion in a…
We use the inverse scattering method to construct classical solutions for the Novikov-Veselov (NV) equation, solving a problem posed by Lassas, Mueller, Siltanen, and Stahel. We exploit Bogadanov's Miura-type map which transforms solutions…
We introduce a novel machine learning based framework for discovering integrable models. Our approach first employs a synchronized ensemble of neural networks to find high-precision numerical solution to the Yang-Baxter equation within a…
There exist many four dimensional integrable theories. They include self-dual gauge and gravity theories, all their extended supersymmetric generalisations, as well the full (non-self-dual) N=3 super Yang-Mills equations. We review the…
We enlarge the spectral problem of a generalized D-Kaup-Newell (D-KN) spectral problem. Solving the enlarged zero-curvature equations, we produce integrable couplings. A reduction of the spectral matrix leads to a second integrable coupling…
A non-isospectral Lax pair is first introduced from which a kind of non-isospectral integrable TD hierarchy is derived, whose reduction is an integrable system called the non-isospectral integrable TD system. Then by using the inverse…
We consider the quantum inverse scattering method for several mixed integrable models based on the rational SU(N) R-matrix with general toroidal boundary conditions. This includes systems whose Hilbert spaces are invariant by the discrete…
We show that all (n-component) KP tau-functions, which are related to the twisted loop group of $GL_n$, give solutions of the Darboux-Egoroff system of PDE's. Using the Geometry of the Grassmannian we construct from the corresponding wave…
In this paper we develop a formalism for working with twisted realizations of vertex and conformal algebras. As an example, we study realizations of conformal algebras by twisted formal power series. The main application of our technique is…
We give a geometric interpretation of all the $m$-th elliptic integrable systems associated to a $k'$-symmetric space $N=G/G_0$ (in the sense of C.L. Terng). It turns out that we have to introduce the integer $m_{k'}$ defined by m_{1}=0 and…
We construct integral forms for the universal enveloping algebras of certain twisted multiloop algebras and explicit integral bases for these integral forms.
This thesis presents two descriptions of complexity in dynamical systems. The algebraic approach deals with the differential Galois group theory and its restrictions on integrability. The geometric part is a formulation of dynamics in the…
We introduce twisted triple crossing diagram maps, collections of points in projective space associated to bipartite graphs on the cylinder, and use them to provide geometric realizations of the cluster integrable systems of Goncharov and…
An integrable field theory, due to path-independence on the space-time plane, should yield together with an infinite set of independent conserved charges also similar dual charges determining the boundary and defect contributions. On the…
We describe some recent development on the theory of formal Frobenius manifolds via a construction from differential Gerstenhaber-Batalin-Vilkovisk (DGBV) algebras and formulate a version of mirror symmetry conjecture: the extended…
In this paper we give a geometrical interpretation of all the second elliptic integrable systems associated to 4-symmetric spaces. We first show that a 4-symmetric space $G/G_0$ can be embedded into the twistor space of the corresponding…
The Teukolsky equations are currently the leading approach for analysing stability of linear massless fields propagating in rotating black holes. It has recently been shown that the geometry of these equations can be understood in terms of…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…