Related papers: Nonlinear Lattices Generated from Harmonic Lattice…
We establish sharp geometric Holder regularity estimates for Gradient for bounded solutions of a class of fully nonlinear elliptic equations with non-homogeneous degeneracy. Such regularity estimates simplify and generalize, to some extent,…
The below-threshold harmonic generation in the multiphoton ionization regime for a helium atom driven by the elliptically polarized laser field is studied numerically within the framework of two-dimensional (2D) and three-dimensional (3D)…
The central idea of this article is to present a systematic approach to construct some recurrence relations for the solutions of the second-order linear difference equation of hypergeometric-type defined on the quadratic-type lattices. We…
The coupled-mode theory is developed for description of the nonlinear wave dynamics in binary optical lattices. The obtained equations of motion accurately describe nonlinear wave dynamics close to the band edges and in the gap of the…
We derive lattice invariants from the heat flux of a lattice. Using systems of harmonic polynomials, we obtain sums of products of spherical theta functions which give new invariants of integer lattices which are modular forms. In…
The multiphase Whitham modulation equations with $N$ phases have $2N$ characteristics which may be of hyperbolic or elliptic type. In this paper a nonlinear theory is developed for coalescence, where two characteristics change from…
In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…
We theoretically study the non-linear response of interacting neutral bosonic gas in a synthetically driven one-dimensional optical lattice. In particular, we examine the bosonic analogue of electronic higher harmonic generation in a strong…
The interplay between real-space topological lattice defects and the reciprocal-space topology of energy bands can give rise to novel phenomena, such as one-dimensional topological modes bound to screw dislocations in three-dimensional…
A straightforward algorithm for the symbolic computation of higher-order symmetries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the…
In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable…
An examples of multidimensional the Ricci-flat spaces defined by nonlinear differential equations are constructed. Their properties are discussed.
Integrated photonic systems provide a flexible platform where artificial lattices can be engineered in a reconfigurable fashion. Here, we show that one-dimensional photonic arrays with engineered losses allow the realization of topological…
Non-Hermitian topological matter provides a platform for engineering phenomena that go beyond the capabilities of Hermitian systems, enabling the use of losses to engineer topological phenomena. Non-Hermitian models often rely on artificial…
Recently, it was shown that strongly driven micromechanical resonators show mode shapes that strongly differ from the eigenmodes. This raises the question of the origin of this nonlinear behavior. We measure the spatial dependence of the…
We develop the theory of nonlinear localised modes (intrinsic localised modes or discrete breathers) in two-dimensional (2D) photonic crystal waveguides. We consider different geometries of the waveguides created by an array of nonlinear…
We consider a variety of settings involving chains with one or more defects stemming from the introduction of nodes bearing internal resonators. Motivated by experimental results in woodpile elastic lattices with one or two defects, we…
Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with…
Interest in the elastic properties of regular lattices constructed from domain walls has recently been motivated by cosmological applications as solid dark energy. This work investigates the particularly simple examples of triangular,…
Non-Hermitian systems can host topological states with novel topological invariants and bulk-edge correspondences that are distinct from conventional Hermitian systems. Here we show that two unique classes of non-Hermitian 2D topological…