On Riemann wave superpositions obtained from the Euler system
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914255899459584 |
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| author | Chomienia, Łukasz Grundland, Alfred Michel |
| author_facet | Chomienia, Łukasz Grundland, Alfred Michel |
| contents | The paper contains an analysis of the conditions for the existence of elastic versus non-elastic wave superpositions governed by the Euler system in (1+1)-dimensions. A review of recently obtained results is presented, including the introduction of the notion of quasi-rectifiability of vector fields and its application to both elastic and non-elastic wave superpositions. It is shown that the smallest real Lie algebra containing vector fields associated with the waves admitted by the Euler system is isomorphic to an infinite-dimensional Lie algebra which is the semi-direct sum of an Abelian ideal and the three-dimensional real Lie algebra. The maximal Lie module corresponding to the Euler system can be transformed, by an angle preserving transformation, to this algebra which is quasi-rectifiable and describes the behavior of wave superpositions. Based on these facts, we are able to find a parametrization of the region of non-elastic wave superpositions which allows for the construction of the reduced form of the Euler system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09576 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Riemann wave superpositions obtained from the Euler system Chomienia, Łukasz Grundland, Alfred Michel Mathematical Physics Analysis of PDEs 35Q31, 35A30, 17B80, 53A05 The paper contains an analysis of the conditions for the existence of elastic versus non-elastic wave superpositions governed by the Euler system in (1+1)-dimensions. A review of recently obtained results is presented, including the introduction of the notion of quasi-rectifiability of vector fields and its application to both elastic and non-elastic wave superpositions. It is shown that the smallest real Lie algebra containing vector fields associated with the waves admitted by the Euler system is isomorphic to an infinite-dimensional Lie algebra which is the semi-direct sum of an Abelian ideal and the three-dimensional real Lie algebra. The maximal Lie module corresponding to the Euler system can be transformed, by an angle preserving transformation, to this algebra which is quasi-rectifiable and describes the behavior of wave superpositions. Based on these facts, we are able to find a parametrization of the region of non-elastic wave superpositions which allows for the construction of the reduced form of the Euler system. |
| title | On Riemann wave superpositions obtained from the Euler system |
| topic | Mathematical Physics Analysis of PDEs 35Q31, 35A30, 17B80, 53A05 |
| url | https://arxiv.org/abs/2510.09576 |