Brunhuber C, Mertens F G, Gaididei Y
Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jan;73(1 Pt 2):016614. doi: 10.1103/PhysRevE.73.016614. Epub 2006 Jan 24.
We investigate the influence of dissipation on envelope solitons on anharmonic chains. We consider both Stokes and hydrodynamical damping and derive the evolution equations for the envelope in both the continuum and the quasi-continuum approximation of the chain. We introduce an appropriate collective variable ansatz for the envelope in order to describe the effect of damping on the soliton shape. We derive ordinary differential equations for the evolution of the three collective variables amplitude, width, and chirp which describe the spatial modulation of the envelope. The analytical results are in good agreement with the simulations of the discrete system for high-energy excitations on the chain. Our results derived from the quasi-continuum approximation show significant improvements compared to the continuum approximation.
我们研究了耗散对非谐链上包络孤子的影响。我们考虑了斯托克斯阻尼和流体动力学阻尼，并在链的连续介质近似和准连续介质近似中推导了包络的演化方程。为了描述阻尼对孤子形状的影响，我们为包络引入了一个合适的集体变量假设。我们推导了描述包络空间调制的三个集体变量——振幅、宽度和啁啾——演化的常微分方程。对于链上的高能激发，解析结果与离散系统的模拟结果吻合良好。我们从准连续介质近似中得到的结果与连续介质近似相比有显著改进。
