TITLE:
The Rise of Solitons in Sine-Gordon Field Theory: From Jacobi Amplitude to Gudermannian Function
AUTHORS:
Leonardo Mondaini
KEYWORDS:
Solitons, Sine-Gordon Field Theory, Elliptic Integrals, Jacobi Amplitude
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.2 No.13,
December
23,
2014
ABSTRACT: We show how the famous soliton solution of the classical sine-Gordon
field theory in (1 + 1)-dimensions may be obtained as a particular case of a
solution expressed in terms of the Jacobi amplitude, which is the inverse
function of the incomplete elliptic integral of the first kind.