Avinash K, Zhu P, Nosenko V, Goree J
Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Oct;68(4 Pt 2):046402. doi: 10.1103/PhysRevE.68.046402. Epub 2003 Oct 8.
A modified Korteweg-de Vries (KdV) equation is obtained for studying the propagation of nonlinear compressional waves and pulses in a chain of particles including the effect of damping. Suitably altering the linear phase velocity makes this equation useful also for the problem of phonon propagation in a two-dimensional (2D) lattice. Assuming a Yukawa potential, we use this method to model compressional wave propagation in a 2D plasma crystal, as in a recent experiment. By integrating the modified KdV equation the pulse is allowed to evolve, and good agreement with the experiment is found. It is shown that the speed of a compressional pulse increases with its amplitude, while the speed of a rarefactive pulse decreases. It is further discussed how the drag due to the background gas has a crucial role in weakening nonlinear effects and preventing the emergence of a soliton.
为了研究包含阻尼效应的粒子链中非线性压缩波和脉冲的传播，得到了一个修正的科特韦格 - 德弗里斯（KdV）方程。适当地改变线性相速度使该方程也适用于二维（2D）晶格中的声子传播问题。假设采用 Yukawa 势，我们使用此方法对二维等离子体晶体中的压缩波传播进行建模，如同最近的一个实验那样。通过对修正的 KdV 方程进行积分，使脉冲得以演化，并且发现与实验结果吻合良好。结果表明，压缩脉冲的速度随其振幅增加，而稀疏脉冲的速度则减小。进一步讨论了背景气体引起的阻力如何在减弱非线性效应和防止孤子出现方面起到关键作用。
