Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management
- Amherst College, MA (United States)
- Univ. of Salerno (Italy)
- Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- International Islamic Univ. of Malaysia (Malaysia)
The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined. We also found that other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. Finally, the possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1234821
- Report Number(s):
- LA-UR--15-26190
- Journal Information:
- Physical Review A - Atomic, Molecular, and Optical Physics, Journal Name: Physical Review A - Atomic, Molecular, and Optical Physics Journal Issue: 5 Vol. 92; ISSN 1050-2947; ISSN PLRAAN
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Kinks and branes in models with hyperbolic interactions
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journal | September 2017 |
| Kinks and branes in models with hyperbolic interactions | text | January 2017 |
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