Related papers: Veronese webs and nonlinear PDEs
Carbon-elastomer composites exhibit complex piezoresistive behaviour that cannot be fully explained by existing macroscopic or microstructural models. In this work, we introduce a network-based modelling methodology to explore the…
The three integrable two-dimensional Henon-Heiles systems and their integrable perturbations are revisited. A family of new integrable perturbations is found, and N-dimensional completely integrable generalizations of all these systems are…
We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…
We provide exact analytical solutions for a two dimensional explicitly time-dependent non-Hermitian quantum system. While the time-independent variant of the model studied is in the broken PT-symmetric phase for the entire range of the…
Using topological band theory analysis we show that the nonsymmorphic symmetry operations in hexagonal lattices enforce Weyl points at the screw-invariant high-symmetry lines of the band structure. The corepresentation theory and…
The isolation of a growing number of two-dimensional (2D) materials has inspired worldwide efforts to integrate distinct 2D materials into van der Waals (vdW) heterostructures. Given that any passivated, dangling bond-free surface will…
The membrane model is a Gaussian interface model with a Hamiltonian involving second derivatives of the interface height. We consider the model in dimension $\mathsf{d}\ge4$ under the influence of $\delta$-pinning of strength $\varepsilon$.…
A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of $\delta$-pseudo-differential operators, valid on an arbitrary regular time scale, is…
We give a new proof for the parabolic Verlinde formula in all ranks based on a comparison of wall-crossings in Geometric Invariant Theory and certain iterated residue functionals. On the way, we develop a tautological variant of Hecke…
In the complex setting, let $F(x,y,y')=0$ be an analytic or algebraic differential equation with $y'$-degree $d$. We deal with the qualitative study of such equations through the geometry of the planar $d$-web generated by the generic…
Vertical stacking of two-dimensional (2D) crystals, such as graphene and hexagonal boron nitride, has recently lead to a new class of materials known as van der Waals heterostructures (vdWHs) with unique and highly tunable electronic…
We study the relations between the projective and the almost conformally symplectic structures on a smooth even dimensional manifold. We describe these relations by a single almost conformally symplectic connection with totally trace--free…
All local solutions of the two dimensional Einstein-Weyl equations are found, and related to the compact examples which I obtained in "Moebius structures and two dimensional Einstein-Weyl geometry" J. reine angew. Math. 504 (1998).
We review the results of several of our papers about the procedure of extension of Hamiltonians, allowing the construction of families of superintegrable systems with non-trivial polynomial first integrals (or symmetry operators) of…
By incorporating higher-form symmetries, we propose a refined definition of the theories obtained by compactification of the 6d $(2,0)$ theory on a three-manifold $M_3$. This generalization is applicable to both the 3d $\mathcal{N}=2$ and…
The general solution of SUSY intertwining relations for three-dimensional Schr\"odinger operators is built using the class of second order supercharges with nondegenerate constant metric. This solution includes several models with arbitrary…
Holonomy algebras of Lorentzian Weyl spin manifolds with weighted parallel spinors are found. For Lorentzian Weyl manifolds admitting recurrent null vector fields are introduced special local coordinates similar to Kundt and Walker ones.…
We address the electronic structure of quantum wells in polar-nonpolar oxide heterojunction systems focusing on the case of non-polar BaVO$_3$ wells surrounded by polar LaTiO$_3$ barriers. Our discussion is based on a density functional…
We present recent developments on geometric theory of the Hirota system and of the non-commutative discrete Kadomtsev-Petviashvili (KP) hierarchy adding also some new results which make the picture more complete. We pay special attention to…
The survey is devoted to algebraic structures related to integrable ODEs and evolution PDEs. A description of Lax representations is given in terms of vector space decomposition of loop algebras into a direct sum of Taylor series and a…