The Rise of Solitons in Sine-Gordon Field Theory: From Jacobi Amplitude to Gudermannian Function

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.

To appear in J. Appl. Math. Phys., 7 pages

References in corpus (2)

• Vanishing conductivity of quantum solitons in polyacetylene
• Thermal soliton correlation functions in theories with a Z(N) symmetry