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.

Highlights

  • The sine-Gordon field theory and the associated massive Thirring model [1] are some of the best studied quantum field theories

  • In view of its connections to other important physical models, some of which in principle admit actual realizations in nature [2] [3], a huge mass of important exact results have been obtained for this fascinating integrable system [4]-[7]

  • In this work we present a simple and yet appealing step-by-step derivation of a more general solution for the classical sine-Gordon field theory in (1 + 1)-dimensions in terms of a special kind of elliptic function, namely the Jacobi amplitude, which has the famous sine-Gordon soliton solution as a particular case

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Summary

Introduction

The sine-Gordon field theory and the associated massive Thirring model [1] are some of the best studied quantum field theories. In this work we present a simple and yet appealing step-by-step derivation of a more general solution for the classical sine-Gordon field theory in (1 + 1)-dimensions in terms of a special kind of elliptic function, namely the Jacobi amplitude, which has the famous sine-Gordon soliton solution as a particular case. Despite the fact that the connection between solitons and Jacobi elliptic functions has already been explored in [8], we believe that this work comes to shed more light on this interesting subject, helping to fill in a gap existing in the corres-. (2014) The Rise of Solitons in Sine-Gordon Field Theory: From Jacobi Amplitude to Gudermannian Function.

The Jacobi Amplitude Function
Concluding Remarks
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