Two-dimensional solitons and vortices in media with incommensurate linear and nonlinear lattice potentials

Abstract

We construct families of ordinary and gap solitons (GSs), including solitary vortices, in the two-dimensional (2D) system based on the nonlinear-SchrÄodinger/Gross-Pitaevskii equation with the 2D or quasi-1D (Q1D) periodic linear potential, combined with the periodic modulation of the cubic nonlinearity (also in the 2D or Q1D form), which is, generally, incommensurate with the linear potential, thus forming a \nonlinear quasicrystal". Stable vortices are built as complexes of four peaks with the separation between them equal to the double period of the linear potential. The system may be realized in photonic crystals or Bose-Einstein condensates (BECs). The variational approximation (VA) is applied to ordinary solitons (residing in the semi-infinite gap), and numerical methods are used to construct solitons of all the types. Stability regions are identified for soliton families in all the versions of the model.

8 pages, 11 figures. Accepted for a Special issue on Photonics of Physica Scripta

References in corpus (5)

• Solitons in nonlinear lattices
• Spontaneous symmetry breaking in a nonlinear double-well structure
• Gap solitons in quasiperiodic optical lattices
• Surface solitons at interfaces of arrays with spatially-modulated nonlinearity
• Matter-wave 2D solitons in crossed linear and nonlinear optical lattices

Cited by in corpus (11)

• One-dimensional solitons in fractional Schrödinger equation with a spatially modulated nonlinearity: nonlinear lattice
• One-dimensional gap solitons in quintic and cubic-quintic Fractional nonlinear Schrödinger equations with a periodically modulated linear potential
• Gap-type dark localized modes in a Bose-Einstein condensate with optical lattices
• Bright solitons in defocusing media with spatial modulation of the quintic nonlinearity
• Photon-atomic solitons in a Bose-Einstein condensate trapped in a soft optical lattice
• Gaussian-like and flat-top solitons of atoms with spatially modulated repulsive interactions
• Suppression of the critical collapse for one-dimensional solitons by saturable quintic nonlinear lattices
• Localized modes in nonlinear fractional systems with deep lattices
• Two-dimensional intra-band solitons in lattice potentials with local defects and self-focusing nonlinearity
• Self-trapped spatially localized states in combined linear-nonlinear periodic potentials
• Towards the complete description of stationary states of a Bose-Einstein condensate in a one-dimensional quasiperiodic lattice: A coding approach