LATTICE DYNAMICS ON LARGE TIME SCALES AND DISPERSIVE EFFECTIVE EQUATIONS

被引：3
作者：
Schweizer, Ben [1 ]
Theil, Florian [2 ]
机构：
[1] TU Dortmund, Fak Math, D-44227 Dortmund, Nrw, Germany
[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England
来源：
SIAM JOURNAL ON APPLIED MATHEMATICS | 2018年 / 78卷 / 06期
关键词：
lattice dynamics; continuum limit; dispersive effective equation; WAVE-PROPAGATION; HETEROGENEOUS MEDIA; MODELS;
D O I：
10.1137/17M1162184
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate the long time behavior of waves in crystals. Starting from a linear wave equation on a discrete lattice with periodicity epsilon > 0, we derive the continuum limit equation for time scales of order epsilon(-2). The effective equation is a weakly dispersive wave equation of fourth order. Initial values with bounded support result in ring-like solutions, and we characterize the dispersive long time behavior of the radial profiles with a linearized KdV equation of third order.
引用
收藏
页码：3060 / 3086
页数：27
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