On a generalization of Jacobi's elliptic functions and the Double Sine-Gordon kink chain

TL;DR

This paper introduces a generalized form of Jacobi's elliptic functions based on hyperelliptic integrals, explores their properties, and applies them to describe periodic kink solutions in the double sine-Gordon model.

Contribution

It presents a novel generalization of Jacobi's elliptic functions and demonstrates their application to modeling kink chains in the double sine-Gordon system.

Findings

Generalized Jacobi functions are inversions of hyperelliptic integrals.

Addition theorems and indefinite integrals for these functions are derived.

Periodic kink solutions are expressed in terms of the generalized functions.

Abstract

A generalization of Jacobi's elliptic functions is introduced as inversions of hyperelliptic integrals. We discuss the special properties of these functions, present addition theorems and give a list of indefinite integrals. As a physical application we show that periodic kink solutions (kink chains) of the double sine-Gordon model can be described in a canonical form in terms of generalized Jacobi functions.