skip to main content

DOE PAGESDOE PAGES

Title: Solitons and vortices in two-dimensional discrete nonlinear Schrödinger systems with spatially modulated nonlinearity

We consider a two-dimensional (2D) generalization of a recently proposed model [Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the center to the periphery. We explore the 2D model starting from the anticontinuum (AC) limit of vanishing coupling. In this limit, we can construct a wide variety of solutions including not only single-site excitations, but also dipole and quadrupole ones. Additionally, two separate families of solutions are explored: the usual “extended” unstaggered bright solitons, in which all sites are excited in the AC limit, with the same sign across the lattice (they represent the most robust states supported by the lattice, their 1D counterparts being those considered as 1D bright solitons in the above-mentioned work), and the vortex cross, which is specific to the 2D setting. For all the existing states, we explore their stability (also analytically, when possible). As a result, typical scenarios of instability development are exhibited through direct simulations.
Authors:
 [1] ;  [2] ;  [3] ;  [3] ;  [4]
  1. Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Tel Aviv Univ., Tel Aviv (Israel)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  4. Univ. of Athens, Athens (Greece)
Publication Date:
OSTI Identifier:
1233233
Report Number(s):
LA--UR-14-29476
Journal ID: ISSN 1539-3755; PLEEE8
Grant/Contract Number:
NSF-DMS-1312856; FA950-12-1-0332; IRSES605096; 2010239; AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)
Additional Journal Information:
Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print); Journal Volume: 91; Journal Issue: 4; Journal ID: ISSN 1539-3755
Publisher:
American Physical Society (APS)
Research Org:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING