One-Parameter Family of Elliptic Sine-Gordon Equations
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914439446396928 |
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| author | Khare, Avinash Saxena, Avadh |
| author_facet | Khare, Avinash Saxena, Avadh |
| contents | We introduce a continuous one-parameter family of elliptic sine-Gordon equations (SGE) characterized by the modulus $0 \le m \le 1$ of Jacobi elliptic functions and analyze some of its properties and obtain its kink solution for various values of modulus $m$. These elliptic SGE have the novel property that while in the limit $m = 0$ they go over to the integrable sine-Gordon equation, in the $m = 1$ limit they go over to the integrable sine hyperbolic-Gordon equations (SHGE). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01663 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | One-Parameter Family of Elliptic Sine-Gordon Equations Khare, Avinash Saxena, Avadh Pattern Formation and Solitons Mathematical Physics Exactly Solvable and Integrable Systems We introduce a continuous one-parameter family of elliptic sine-Gordon equations (SGE) characterized by the modulus $0 \le m \le 1$ of Jacobi elliptic functions and analyze some of its properties and obtain its kink solution for various values of modulus $m$. These elliptic SGE have the novel property that while in the limit $m = 0$ they go over to the integrable sine-Gordon equation, in the $m = 1$ limit they go over to the integrable sine hyperbolic-Gordon equations (SHGE). |
| title | One-Parameter Family of Elliptic Sine-Gordon Equations |
| topic | Pattern Formation and Solitons Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2604.01663 |