Lahiri Avijit, Panda Subhendu, Roy Tarun K
Department of Physics, Vidyasagar Evening College, Kolkata 700 006, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Nov;66(5 Pt 2):056603. doi: 10.1103/PhysRevE.66.056603. Epub 2002 Nov 18.
Following our earlier work [Phys. Rev. Lett. 84, 3570 (2000)] we present an exact linear stability analysis of one-site monochromatic breathers in a piecewise smooth discrete nonlinear Schrödinger-type model. Destabilization of the breather occurs by virtue of a growth rate becoming positive as a stability border is crossed, while above a critical spatial decay rate (lambda(c)) the breather is found to be intrinsically unstable. The model admits of other exact breather solutions, including multisite monochromatic breathers for which the profile variable (phi(n)) crosses a relevant threshold at more than one site. In particular, we consider exact two-site breather solutions with phase difference delta between the two sites above threshold, and present stability results for delta=pi (antiphase breather; the in-phase breather with delta=0 happens to be intrinsically unstable). We obtain a band of extended eigenmodes, together with a pair of localized symmetric modes and another pair of localized antisymmetric ones. The frequencies of the localized modes vary as the parameters characterizing the breather are made to vary, and destabilization occurs through the Krein collision of a quartet of growth rates, leading to temporal growth of a pair of symmetric eigenmodes of nonzero frequency. We clarify the limit N--> infinity (N is the gap length between the sites above threshold) when the two-site breather reduces to a pair of decoupled one-site breathers. The model offers the possibility of obtaining spatially random vortex-type breathers.
继我们早期的工作[《物理评论快报》84, 3570 (2000)]之后，我们给出了一个分段光滑离散非线性薛定谔型模型中，单格点单色呼吸子的精确线性稳定性分析。当跨越稳定性边界时，增长率变为正值，呼吸子发生失稳，而当空间衰减率超过临界值（λ(c)）时，呼吸子被发现本质上是不稳定的。该模型还存在其他精确的呼吸子解，包括多格点单色呼吸子，其轮廓变量（φ(n)）在多个格点处越过相关阈值。特别地，我们考虑两个格点间相位差为δ的精确双格点呼吸子解，且δ大于阈值，并给出了δ = π时（反相呼吸子；δ = 0的同相呼吸子本质上是不稳定的）的稳定性结果。我们得到了一组扩展本征模，以及一对局域对称模和另一对局域反对称模。当表征呼吸子的参数变化时，局域模的频率也随之变化，失稳通过一组四个增长率的克莱因碰撞发生，导致一对非零频率对称本征模的时间增长。我们阐明了双格点呼吸子退化为一对解耦的单格点呼吸子的极限情况N→∞（N是阈值以上格点间的间距）。该模型提供了获得空间随机涡旋型呼吸子的可能性。
