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arXiv · 2604.01663

One-Parameter Family of Elliptic Sine-Gordon Equations

Avinash Khare·Avadh Saxena
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Abstract

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).

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Avinash Khare, Avadh Saxena. 2026-04-02. One-Parameter Family of Elliptic Sine-Gordon Equations. https://arxiv.org/abs/2604.01663

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