Solitons and vortices in two-dimensional discrete nonlinear Schrödinger systems with spatially modulated nonlinearity
Abstract
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:
-
- Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Tel Aviv Univ., Tel Aviv (Israel)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of Athens, Athens (Greece)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1233233
- Alternate Identifier(s):
- OSTI ID: 1179350
- 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
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
- Additional Journal Information:
- Journal Volume: 91; Journal Issue: 4; Journal ID: ISSN 1539-3755
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Kevrekidis, P. G., Malomed, Boris A., Saxena, Avadh, Bishop, A. R., and Frantzeskakis, D. J. Solitons and vortices in two-dimensional discrete nonlinear Schrödinger systems with spatially modulated nonlinearity. United States: N. p., 2015.
Web. doi:10.1103/PhysRevE.91.043201.
Kevrekidis, P. G., Malomed, Boris A., Saxena, Avadh, Bishop, A. R., & Frantzeskakis, D. J. Solitons and vortices in two-dimensional discrete nonlinear Schrödinger systems with spatially modulated nonlinearity. United States. https://doi.org/10.1103/PhysRevE.91.043201
Kevrekidis, P. G., Malomed, Boris A., Saxena, Avadh, Bishop, A. R., and Frantzeskakis, D. J. Tue .
"Solitons and vortices in two-dimensional discrete nonlinear Schrödinger systems with spatially modulated nonlinearity". United States. https://doi.org/10.1103/PhysRevE.91.043201. https://www.osti.gov/servlets/purl/1233233.
@article{osti_1233233,
title = {Solitons and vortices in two-dimensional discrete nonlinear Schrödinger systems with spatially modulated nonlinearity},
author = {Kevrekidis, P. G. and Malomed, Boris A. and Saxena, Avadh and Bishop, A. R. and Frantzeskakis, D. J.},
abstractNote = {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.},
doi = {10.1103/PhysRevE.91.043201},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
number = 4,
volume = 91,
place = {United States},
year = {Tue Apr 07 00:00:00 EDT 2015},
month = {Tue Apr 07 00:00:00 EDT 2015}
}
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Works referencing / citing this record:
One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential
journal, September 2019
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