Historical note: On the simulation of dispersive wave propagation by elasticity models

Abstract

Attention is called to E. Schrödinger's elegant analytical solution [Annalen der Physik 44 (1914) p.916] of the initial-value problem for the Born–von Kármán model of an infinite one-dimensional chain of uniformly spaced particles of mass M with nearest-neighbour coupling by harmonic springs. This model has recently served as the starting point for a computer study of the transition to partial differential equations describing dispersive wave propagation in inhomogeneous media [Askes et al., Phil. Mag. 88 (2008) p.3415]. Schrödinger's solution allows the main features of the limit process involved in this transition to be studied in a straightforward way.

Keywords:

• dispersive wave propagation
• Born–von Kármán model
• Schrödinger's solution
• transition to generalised continua