Einstein, $σ$-model and Ernst-type equations and non-isospectral GBDT version of Darboux transformation
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866911821718355968 |
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| author | Sakhnovich, Alexander |
| author_facet | Sakhnovich, Alexander |
| contents | We present a non-isospectral GBDT version of Bäcklund-Darboux transformation for the gravitational and $σ$-model equations. New families of explicit solutions correspond to the case of GBDT with non-diagonal generalized matrix eigenvalues. An interesting integrable Ernst-type system, the auxiliary linear systems of which are non-isospectral canonical systems, is studied as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_13024 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Einstein, $σ$-model and Ernst-type equations and non-isospectral GBDT version of Darboux transformation Sakhnovich, Alexander Analysis of PDEs General Relativity and Quantum Cosmology Mathematical Physics Spectral Theory 35Q51, 35Q76, 83C15, 37J05 We present a non-isospectral GBDT version of Bäcklund-Darboux transformation for the gravitational and $σ$-model equations. New families of explicit solutions correspond to the case of GBDT with non-diagonal generalized matrix eigenvalues. An interesting integrable Ernst-type system, the auxiliary linear systems of which are non-isospectral canonical systems, is studied as well. |
| title | Einstein, $σ$-model and Ernst-type equations and non-isospectral GBDT version of Darboux transformation |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology Mathematical Physics Spectral Theory 35Q51, 35Q76, 83C15, 37J05 |
| url | https://arxiv.org/abs/2003.13024 |