Integrable semi-discretizations of the sine-Gordon equation in non-characteristic coordinates
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918264611799040 |
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| author | Tsuchida, Takayuki |
| author_facet | Tsuchida, Takayuki |
| contents | Integrable discretizations of the sine-Gordon equation in characteristic (or light-cone) coordinates have been extensively studied after the seminal works of Hirota and Orfanidis in the late 1970s. In contrast, integrable discretizations of the sine-Gordon equation in non-characteristic coordinates have been scarcely studied except the lattice sine-Gordon model proposed by Izergin and Korepin in the early 1980s. In this paper, using the zero-curvature representation, we propose integrable space discretizations of the sine-Gordon equation in three distinct cases of non-characteristic coordinates. For the most interesting case of the sine-Gordon equation in laboratory coordinates, the integrable space discretization is unwieldy; as a remedy, we rewrite the sine-Gordon equation as a two-component evolutionary system and present an aesthetically acceptable space discretization. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_22919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrable semi-discretizations of the sine-Gordon equation in non-characteristic coordinates Tsuchida, Takayuki Exactly Solvable and Integrable Systems Integrable discretizations of the sine-Gordon equation in characteristic (or light-cone) coordinates have been extensively studied after the seminal works of Hirota and Orfanidis in the late 1970s. In contrast, integrable discretizations of the sine-Gordon equation in non-characteristic coordinates have been scarcely studied except the lattice sine-Gordon model proposed by Izergin and Korepin in the early 1980s. In this paper, using the zero-curvature representation, we propose integrable space discretizations of the sine-Gordon equation in three distinct cases of non-characteristic coordinates. For the most interesting case of the sine-Gordon equation in laboratory coordinates, the integrable space discretization is unwieldy; as a remedy, we rewrite the sine-Gordon equation as a two-component evolutionary system and present an aesthetically acceptable space discretization. |
| title | Integrable semi-discretizations of the sine-Gordon equation in non-characteristic coordinates |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2512.22919 |