Share This Article:

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

Abstract Full-Text HTML XML Download Download as PDF (Size:2774KB) PP. 1202-1206
DOI: 10.4236/jamp.2014.213141    3,632 Downloads   4,030 Views   Citations
Author(s)    Leave a comment


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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Mondaini, L. (2014) The Rise of Solitons in Sine-Gordon Field Theory: From Jacobi Amplitude to Gudermannian Function. Journal of Applied Mathematics and Physics, 2, 1202-1206. doi: 10.4236/jamp.2014.213141.


[1] Coleman, S. (1975) Quantum Sine-Gordon Equation as the Massive Thirring Model. Physical Review D, 11, 2088-2097.
[2] Kosterlitz, J.M. (1974) The Critical Properties of the Two-Dimensional XY Model. Journal of Physics C: Solid State Physics, 7, 1046-1060.
[3] Samuel, S. (1978) Grand Partition Function in Field Theory with Applications to Sine-Gordon Field Theory. Physical Review D, 18, 1916-1932.
[4] Dauxois, T. and Peyrard, M. (2006) Physics of Solitons. Cambridge University Press, New York.
[5] Mondaini, L. and Marino, E.C. (2005) Sine-Gordon/Coulomb Gas Soliton Correlation Functions and an Exact Evaluation of the Kosterlitz-Thouless Critical Exponent. Journal of Statistical Physics, 118, 767-779.
[6] Mondaini, L., Marino, E.C. and Schmidt, A.A. (2009) Vanishing Conductivity of Quantum Solitons in Polyacetylene. Journal of Physics A: Mathematical and Theoretical, 42, Article ID: 055401.
[7] Mondaini, L. (2012) Thermal Soliton Correlation Functions in Theories with a Z(N) Symmetry. Journal of Modern Physics, 3, 1776-1780.
[8] Cervero, J.M. (1986) Unveiling the Solitons Mistery: The Jacobi Elliptic Functions. American Journal of Physics, 54, 35-38.
[9] Mondaini, L. (2012) Obtaining a Closed-Form Representation for the Dual Bosonic Thermal Green Function by Using Methods of Integration on the Complex Plane. Revista Brasileira de Ensino de Física, 34, 3305.
[10] Jackiw, R. (1977) Quantum Meaning of Classical Field Theory. Reviews of Modern Physics, 49, 681-706.
[11] Rajaraman, R. (1987) Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory. Elsevier, Amsterdam.
[12] Gradshteyn, I.S. and Ryzhik, I.M. (2000) Table of Integrals, Series, and Products. Academic Press, San Diego.
[13] Weisstein, E.W. Jacobi Amplitude. MathWorld—A Wolfram Web Resource.

comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.