Richness or Semi-Hamiltonicity of quasi-linear systems which are not in evolution form
Abstract
The aim of this paper is to consider quasi-linear systems which are not in the form of evolution equations. We propose new condition of Richness or Semi-Hamiltonicity for such a system and prove that the blow up analysis along characteristic curves can be performed for it in an analogous manner. This opens a possibility to use this ansatz also for geometric problems. We apply the results to the problem of Polynomial integral for geodesic flows on the 2-torus.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2011
- DOI:
- 10.48550/arXiv.1101.5897
- arXiv:
- arXiv:1101.5897
- Bibcode:
- 2011arXiv1101.5897M
- Keywords:
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- Mathematics - Analysis of PDEs;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems