Bale Brandon G, Kutz J Nathan
Photonics Research Group, Aston University, Birmingham B4 7ET, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Apr;79(4 Pt 2):046602. doi: 10.1103/PhysRevE.79.046602. Epub 2009 Apr 6.
A theoretical model shows that in the context of a Ginzburg-Landau equation with rapidly varying, mean-zero dispersion, stable and attracting self-similar breathers are formed with parabolic profiles. These self-similar solutions are the final solution state of the system, not a long-time, intermediate asymptotic behavior. A transformation shows the self-similarity to be governed by a nonlinear diffusion equation with a rapidly varying, mean-zero diffusion coefficient. The alternating sign of the diffusion coefficient, which is driven by the dispersion fluctuations, is critical to supporting the parabolic profiles which are, to leading order, of the Barenblatt form. Our analytic model proposes a mechanism for generating physically realizable temporal parabolic pulses in the Ginzburg-Landau model.
一个理论模型表明，在具有快速变化的、均值为零的色散的金兹堡 - 朗道方程的背景下，会形成具有抛物线型轮廓的稳定且有吸引力的自相似呼吸子。这些自相似解是系统的最终解状态，而非长时间的中间渐近行为。一种变换表明，自相似性由一个具有快速变化的、均值为零的扩散系数的非线性扩散方程所支配。由色散涨落驱动的扩散系数的交替符号，对于支持抛物线型轮廓至关重要，这些抛物线型轮廓在主导阶上具有巴伦布拉特形式。我们的解析模型提出了一种在金兹堡 - 朗道模型中生成物理上可实现的时间抛物线型脉冲的机制。
