Related papers: Homogeneous Backlund transformations of hyperbolic…
Let $M$ be an irreducible holomorphic symplectic (hyperk\"ahler) manifold. If $b_2(M)\geq 5$, we construct a deformation $M'$ of $M$ which admits a symplectic automorphism of infinite order. This automorphism is hyperbolic, that is, its…
We study the long-time existence and convergence of general parabolic complex Monge-Ampere type equations whose second order operator is not necessarily convex or concave in the Hessian matrix of the unknown solution.
We give new Backlund transformations (BTs) for some known integrable (in the sense of being multidimensionally consistent) quadrilateral lattice equations. As opposed to the natural auto-BT inherent in every such equation, these BTs are of…
We establish an explicit form of the Backlund transformation for the most known integrable systems.
Let $M$ be a closed orientable surface of negative curvature. A connection is said to be transparent if its parallel transport along closed geodesics is the identity. We describe all transparent SU(2)-connections and we show that they can…
We consider a long--range homogeneous chain where the local variables are the generators of the direct sum of $N$ $\mathfrak{e}(3)$ interacting Lagrange tops. We call this classical integrable model rational ``Lagrange chain'' showing how…
We consider the St\"ackel transform, also known as the coupling-constant metamorphosis, which under certain conditions turns a Hamiltonian dynamical system into another such system and preserves the Liouville integrability. We show that the…
Binary symmetry constraints are applied to constructing B\"acklund transformations of soliton systems, both continuous and discrete. Construction of solutions to soliton systems is split into finding solutions to lower-dimensional Liouville…
A structure is called homogeneous if every isomorphism between finite substructures of the structure extends to an automorphism of the structure. Recently, P. J. Cameron and J. Ne\v{s}et\v{r}il introduced a relaxed version of homogeneity:…
A uniqueness result in the inverse problem for an inhomogeneous hyperbolic system on a real vector bundle over a smooth compact manifold, based on energy measurements for improperly known sources, is established.
It is shown that there exists two inner authomorpism which lead to different form of the sistems equations of integrable hierarchy. We present discrete and Backlund transformation connected with such systems and a general formula for…
The Neumann and Chaplygin systems on the sphere are simultaneously separable in variables obtained from the standard elliptic coordinates by the proper Backlund transformation. We also prove that after similar Backlund transformations other…
We study the geometric properties of complex manifolds possessing a pair of plurisubharmonic functions satisfying Monge-Amp\`ere type of condition. The results are applied to characterize complex manifolds biholomorphic to $\C^{N}$ viewed…
The classification problem is solved for some type of nonlinear lattices. These lattices are closely related to the lattices of Ruijsenaars-Toda type and define the Backlund auto-transformations for the class of two-component hyperbolic…
We present a B\"acklund transformation (a discrete symmetry transformation) for the self-duality equations for supersymmetric gauge theories in N-extended super-Minkowski space ${\cal M}^{4|4N}$ for an arbitrary semisimple gauge group. For…
A general homogenization procedure for periodic electromagnetic structures, when applied to layered media with asymmetric lattice cells, yields an effective tensor with magnetoelectric coupling. Accurate results for transmission and…
In this work we develop a self-consistent approach for calculation of the Purcell factor and Lamb shift in highly dispersive hyperbolic metamaterial accounting for the effective dipole frequency shift. Also we theoretically predict the…
This paper contains theory on two related topics relevant to manifolds of normally hyperbolic singularities. First, theorems on the formal and $ C^k $ normal forms for these objects are proved. Then, the theorems are applied to give…
For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant…
We present a multiparameter generalization of the St\"ackel transform (the latter is also known as the coupling-constant metamorphosis) and show that under certain conditions this generalized St\"ackel transform preserves the Liouville…