Second-order differential equation associated with contact geometry: Symmetries, conservation laws and shock waves
✍ Scribed by L. Zilbergleit
- Publisher
- Springer Netherlands
- Year
- 1996
- Tongue
- English
- Weight
- 766 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0167-8019
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✦ Synopsis
We describe the structure and the correspondence between contact symmetries and conservation laws for second-order differential equations associated with contact geometry. The construction of the Hugoniot-Rankine conditions on discontinuous solutions (shock waves) in natural terms of symbols and generating functions is given. As an example, we demonstrate our techniques for complete descriptions of the infinite-dimensional algebra of contact symmetries and the infinite-dimensional ideal of conservation laws for the von K~irmfm equation in gas and hydrodynamics, as well as for the construction of 4-parametric discontinuous solutions (shock waves) with a spiral rotation on boundary surfaces (shock wave front sets).