Related papers: Surface Solitons in Three Dimensions
We study the stability and structure of vortices emerging in two-dimensional quantum dots in high magnetic fields. Our results obtained with exact diagonalization and density-functional calculations show that vortex structures can be found…
Recent highly idealized model studies of lubricated nanofriction for two crystalline sliding surfaces with an interposed thin solid crystalline lubricant layer showed that the overall relative velocity of the lubricant $v_{\rm lub} / v_{\rm…
A periodic surface is one that is invariant by a 2D lattice of translations. Deformation modes that stretch the lattice without stretching the surface are effective membrane modes. Deformation modes that bend the lattice without stretching…
We show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, give rise to completely localized spatiotemporal solitons (vortex tori) with vorticity…
We study the stabilization of localized structures by discreteness in one-dimensional lattices of diffusively coupled nonlinear sites. We find that in an external driving field these structures may lose their stability by either relaxing to…
Stability of off-site vortex solitons in a photorefractive optical lattice is analyzed. It is shown that such solitons are linearly unstable in both the high and low intensity limits. In the high-intensity limit, the vortex looks like a…
The nonlinear lattice---a new and nonlinear class of periodic potentials---was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic…
We find three distinct phases; a tubular phase, a planar phase, and the spherical phase, in a triangulated fluid surface model. It is also found that these phases are separated by discontinuous transitions. The fluid surface model is…
We study two-color surface solitons in two-dimensional photonic lattices with quadratic nonlinear response. We demonstrate that such parametrically coupled optical localized modes can exist in the corners or at the edges of a square…
We study the properties of surface solitons generated at the edge of a semi-infinite photonic lattice in nonlinear quadratic media, namely two-color surface lattice solitons. We analyze the impact of phase mismatch on existence and…
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of…
Nonlinearities can have a profound influence on the dynamics and equilibrium properties of discrete lattice systems. The simple case of two coupled modes with self-nonlinearities gives rise to the rich bosonic Josephson effects. In…
We study the ground-state physics of a single-component Haldane model on a hexagonal two-leg ladder geometry with a particular focus on strongly interacting bosonic particles. We concentrate our analysis on the regime of less than one…
We report that defocusing cubic media with spatially inhomogeneous nonlinearity, whose strength increases rapidly enough toward the periphery, can support stable bright localized modes. Such nonlinearity landscapes give rise to a variety of…
Assume a lower-dimensional solitonic structure embedded in a higher dimensional space, e.g., a 1D dark soliton embedded in 2D space, a ring dark soliton in 2D space, a spherical shell soliton in 3D space etc. By extending the Landau…
A new type of three-dimensional magnetic soliton in easy-axis ferromagnets is predicted by taking simultaneous account of the Dzyaloshinsky-Moriya interaction and an external magnetic field. The numerically obtained static three-dimensional…
In this note, we study deformations of quaternionic hyperbolic lattices in larger quaternionic hyperbolic spaces and prove local rigidity results. On the other hand, surface groups are shown to be more flexible in quaternionic hyperbolic…
In this note, we survey recent advances in the study of dynamical properties of the space of surfaces with constant curvature in three-dimensional manifolds of negative sectional curvature. We interpret this space as a two-dimensional…
The main purpose of this work is to provide a non-local approach to study aspects of structural stability of 3D Filippov systems. We introduce a notion of semi-local structural stability which detects when a piecewise smooth vector field is…
This concise review aims to provide a summary of the most relevant recent experimental and theoretical results for solitons, i.e., self-trapped bound states of nonlinear waves, in two- and three-dimensional (2D and 3D) media. In comparison…