## Abstract In this paper, both the direct method and the non‐classical Lie approach are applied to reduce the (2 + 1)‐dimensional dispersive long wave equations. Nine types of two‐dimensional PDE reductions and 13 types of ODE reductions are given. All the known reductions obtained by the classica
High-order simulation of the elastic–plastic wave equation in two space dimensions
✍ Scribed by Guido Giese; Michael Fey
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 184 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0165-2125
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✦ Synopsis
In this paper, we present a numerical scheme for the simulation of elastic-plastic waves in solids in one and two space dimensions, i.e. for the two cases of so-called anti-plane shear and plane strain. In principle, the method presented can be used for simulations of any order in space and time and for any hysteresis model that allows the description of plastic flow in the form of an ODE. Furthermore, we show numerical results in one and two space dimensions.
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