Discrete breathers in nonlinear Schrödinger hypercubic lattices with arbitrary power nonlinearity
- 作者：J. Dorignac ; J. Zhou ; D.K. Campbell
- 关键词：Discrete nonlinear Schrö ; dinger equation ; Anti-continuum limit ; Exponential ansatz ; Excitation thresholds ; Lattice Green’ ; s functions ; Nonlinear impurity
- 刊名：Physica D
- 出版年：2008
- 期刊代码：55_01672789
- 类别：ph
- 出版时间：April 2008
- 卷：237
- 期：4
- 页码：486-504
- 文件大小：1282 K
摘要
We study two specific features of onsite breathers in Nonlinear Schrödinger systems on f412b3666ea895e477" title="Click to view the MathML source" alt="Click to view the MathML source">d-dimensional cubic lattices with arbitrary power nonlinearity (i.e., arbitrary nonlinear exponent, n): their wavefunctions and energies close to the anti-continuum limit–small hopping limit–and their excitation thresholds. Exact results are systematically compared to the predictions of the so-called exponential ansatz (EA) and to the solution of the single nonlinear impurity model (SNI), where all nonlinearities of the lattice but the central one, where the breather is located, have been removed. In 1D, the exponential ansatz is more accurate than the SNI solution close to the anti-continuum limit, while the opposite result holds in higher dimensions. The excitation thresholds predicted by the SNI solution are in excellent agreement with the exact results but cannot be obtained analytically except in 1D. An EA approach to the SNI problem provides an approximate analytical solution that is asymptotically exact as n tends to infinity. But the EA result degrades as the dimension, d, increases. This is in contrast to the exact SNI solution which improves as n and/or d increase. Finally, in our investigation of the SNI problem we also prove a conjecture by Bustamante and Molina [C.A. Bustamante, M.I. Molina, Phys. Rev. B 62 (23) (2000) 15287] that the limiting value of the bound state energy is universal when n tends to infinity.