Related papers: Integrable systems related to elliptic branched co…
A new integrable lattice system is introduced, and its integrable discretizations are obtained. A B\"acklund transformation between this new system and the Toda lattice, as well as between their discretizations, is established.
For the direct sum of several copies of sl_n, a family of Lie brackets compatible with the initial one is constructed. The structure constants of these brackets are expressed in terms of theta-functions associated with an elliptic curve.…
We find explicitly all bi-umbilical foliated semi-symmetric hypersurfaces in the four-dimensional Euclidean space.
New integrable lattice systems are introduced, their different integrable discretization are obtained. B\"acklund transformations between these new systems and the relativistic Toda lattice (in the both continuous and discrete time…
Given a hyperkahler manifold M, the hyperkahler structure defines a triple of symplectic structures on M; with these, a triple of Hamiltonians defines a so called hyperhamiltonian dynamical system on M. These systems are integrable when can…
Under the merger hypothesis, elliptical galaxies are built through mergers of gas-rich spirals. However, the relative paucity of HI in most normal ellipticals demands significant processing of atomic gas into other forms if this process is…
Some ball-quotient orbifolds are related by covering maps. We exploit these coverings to find infinite towers of orbifolds uniformized by the complex 2-ball and some orbifolds over K3 surfaces uniformized by the 2-ball. Corresponding…
The formalism of integrable mappings is applied to the problem of constructing hierarchies of $(1+2)$ dimensional integrable systems in the $(2|2)$ superspace. We find new supersymmetric integrable mappings and corresponding to them new…
Hex systems were recently introduced [A. P. Kels. Integrable systems on hexagonal lattices and consistency on polytopes with quadrilateral and hexagonal faces. 2022. arXiv:2205.02720 [math-ph]] as systems of equations defined on…
We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated with generalized Kahler, SKT and strong HKT manifolds all naturally admit complex…
We present examples of Lax-integrable multi-dimensional systems of partial differential equations with higher local symmetries. We also consider Lagrangian deformations of these equations and construct variational bivectors on them.
One encounters iterated elliptic integrals in the study of Hall effect devices, as a result of conformal mappings of Schwarz--Christoffel type. Some of these double elliptic integrals possess amazing symmetries with regard to the physical…
Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schr\"odinger family of…
The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry \`a la Hitchin). The generalized twistor space associated to such a manifold is…
We exhibit isomorphisms of Grassmann spaces and their relationship with collineations and embeddings of the underlying projective spaces.
We show that the semigroup associated to a second-order elliptic system is positive if and only if the differential equations are essentially decoupled and the coefficients are real-valued. This means the system can be replaced by an…
We investigate theoretically the ground-state configurations of two-dimensional charged-particle systems with an elliptical hard-wall boundary and their vibrational eigenmodes. The systems exhibit a series of structural transitions, finally…
We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two form in essence an annotated table of the main evaluation and transformation formulas for elliptic…
We show that the space of orthogonally separable coordinates on the sphere $S^3$ induces a natural family of integrable systems, which after symplectic reduction leads to a family of integrable systems on $S^2 \times S^2$. The generic…
Using isophotal radius correlations for a sample of 2MASS ellipticals, we have constructed a series of template surface brightness profiles to describe the profile shapes of ellipticals as a function of luminosity. The templates are a…