Exact quasi-periodic solutions to the sine(sinh)-Gordon equations: The method for computation and analysis
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910167654727680 |
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| author | Bernatska, Julia |
| author_facet | Bernatska, Julia |
| contents | The sine(sinh)-Gordon hierarchy of integrable Hamiltonian systems is described in detail, and all dynamic variables are expressed in terms of the $\wp$-functions that uniformize the associated spectral curve. Quasi-periodic solutions to the sine(sinh)-Gordon equations are obtained
in terms of the function $\wp_{1,2g-1}$, reality conditions are revised,
and a method of computation and analysis
is presented. The proposed method is designed to analyze solutions
by means of the Hamiltonian technique, which is illustrated in genera one and two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07862 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact quasi-periodic solutions to the sine(sinh)-Gordon equations: The method for computation and analysis Bernatska, Julia Exactly Solvable and Integrable Systems Mathematical Physics 37J35, 37J37, 37J38 The sine(sinh)-Gordon hierarchy of integrable Hamiltonian systems is described in detail, and all dynamic variables are expressed in terms of the $\wp$-functions that uniformize the associated spectral curve. Quasi-periodic solutions to the sine(sinh)-Gordon equations are obtained in terms of the function $\wp_{1,2g-1}$, reality conditions are revised, and a method of computation and analysis is presented. The proposed method is designed to analyze solutions by means of the Hamiltonian technique, which is illustrated in genera one and two. |
| title | Exact quasi-periodic solutions to the sine(sinh)-Gordon equations: The method for computation and analysis |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics 37J35, 37J37, 37J38 |
| url | https://arxiv.org/abs/2501.07862 |