Related papers: Miura type transformations and homogeneous spaces

It is suspected that the quantum evolution equations describing the micro-world as we know it are of a special kind that allows transformations to a special set of basis states in Hilbert space, such that, in this basis, the evolution is…

We prove that any potential symmetry of a system of evolution equations reduces to a Lie symmetry through a nonlocal transformation of variables. Based on this fact is our method of group classification of potential symmetries of systems of…

We define a Fourier-Mukai transform for Higgs bundles on smooth curves and study its properties. It is shown that the transform of a stable zero-degree Higgs bundle is an algebraic vector bundle on the cotangent bundle of the Jacobian of…

We present reciprocal transformations for the spectral problems of Korteveg de Vries (KdV) and modified Korteveg de Vries (mKdV) equations. The resulting equations, RKdV (reciprocal KdV) and RmKdV (reciprocal mKdV), are connected through a…

Higher KdV flows on spaces of closed equicentroaffine plane curves are studied and it is shown that the flows are described as certain multi-Hamiltonian systems on the spaces. Multi-Hamiltonian systems describing higher mKdV flows are also…

Among plenty of applications, low-dimensional homogeneous spaces appear in cosmological models as both, classical factor spaces of multidimensional geometry and minisuperspaces in canonical quantization. Here a new tool to restrict their…

We discuss how point transformations can be used for the study of integrability, in particular, for deriving classes of integrable variable-coefficient differential equations. The procedure of finding the equivalence groupoid of a class of…

It is shown that a class of important integrable nonlinear evolution equations in (2+1) dimensions can be associated with the motion of space curves endowed with an extra spatial variable or equivalently, moving surfaces. Geometrical…

Convolution in Borel-Moore homology plays an important role in Nakajima's construction of representations of the Heisenberg algebra and of modified enveloping algebras of Kac-Moody algebras. In its most basic form, convolution between two…

In this paper we explore interconnections of differential-difference matrix Lax representations (Lax pairs), gauge transformations, and discrete Miura-type transformations (MTs), which belong to the main tools in the theory of integrable…

We consider evolution equations of the Lotka-Volterra type, and elucidate especially their formulation as canonical Hamiltonian systems. The general conditions under which these equations admit several conserved quantities…

We study the k-forms of almost homogeneous varieties over perfect base fields k. First, we discuss criteria for the existence of k-forms in the homogeneous case. Then, we extend the Luna-Vust theory from algebraically closed fields to…

An elementary yet remarkable similarity between the Cole-Hopf transformation relating the Burgers and heat equation and Miura's transformation connecting the KdV and mKdV equations is studied in detail.

Symmetric $k$-varieties generalize Riemannian sym\-me\-tric spaces to reductive groups defined over arbitrary fields. For most perfect fields, it is known that symmetric $k$-varieties are in one-to-one correspondence with isomorphy classes…

In this paper we classify all 4+1 cosmological models where the spatial hypersurfaces are connected and simply connected homogeneous Riemannian manifolds. These models come in two categories, multiply transitive and simply transitive…

In the present article we discuss different approaches to cohomological invariants of algebraic groups over a field. We focus on the Tits algebras and on the Rost invariant and relate them to the Morava K-theory. Furthermore, we discuss…

Toric quiver varieties (moduli spaces of quiver representations) are studied. Given a quiver and a weight there is an associated quasiprojective toric variety together with a canonical embedding into projective space. It is shown that for a…

There are considered differential substitutions of the form $v=P(x,u,u_{x})$ for which there exists a differential operator $H=\sum^{k}_{i=0} \alpha_{i} D^{i}_{x}$ such that the differential substitution maps the equation…

We consider the classical \w42 algebra from the integrable system viewpoint. The integrable evolution equations associated with the \w42 algebra are constructed and the Miura maps , consequently modifications, are presented. Modifying the…

We study birational maps among 1) the moduli space of semistable torsion sheaves of Hilbert polynomial $4m+2$ on a smooth quadric surface, 2) the moduli space of semistable torsion sheaves of Hilbert polynomial $m^{2}+3m+2$ on…