One-Parameter Family of Elliptic Sine-Gordon Equations

We introduce a continuous one-parameter family of elliptic sine-Gordon equations characterized by the modulus parameter 0 ≤ m ≤ 1 of Jacobi elliptic functions and analyze some of its properties as well as obtain its kink solutions for various values of the modulus parameter m. These elliptic sine-Gordon equations 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 equation.