One-Parameter Family of Elliptic Sine-Gordon Equations

Avinash Khare; Avadh Saxena

One-Parameter Family of Elliptic Sine-Gordon Equations

Pattern Formation and Solitons 2026-04-03 v1 Mathematical Physics math.MP Exactly Solvable and Integrable Systems

Authors: Avinash Khare , Avadh Saxena

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).

Keywords

elliptic sine-Gordon equation Jacobi elliptic functions kink solution integrable systems modulus parameter

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@article{arxiv.2604.01663,
  title  = {One-Parameter Family of Elliptic Sine-Gordon Equations},
  author = {Avinash Khare and Avadh Saxena},
  journal= {arXiv preprint arXiv:2604.01663},
  year   = {2026}
}

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14 pages, 7 figures

One-Parameter Family of Elliptic Sine-Gordon Equations

Abstract

Keywords

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