Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies

TL;DR

This paper investigates kink-antikink collisions in the double sine-Gordon equation, focusing on resonance frequencies and how they vary with the potential parameter, revealing long-range interactions at small R values.

Contribution

It provides a qualitative explanation of resonance frequency shifts and highlights the effective long-range interactions in the DSG model at small R.

Findings

Resonance frequencies shift with the potential parameter R.

Long-range interactions occur between kink and antikink at small R.

Frequency shift is explained in relation to the discrete level in the kink's potential well.

Abstract

We studied the kink-antikink collision process for the "double sine-Gordon" (DSG) equation in 1+1 dimensions at different values of the potential parameter $R>0$. For small values of $R$ we discuss the problem of resonance frequencies. We give qualitative explanation of the frequency shift in comparison with the frequency of the discrete level in the potential well of isolated kink. We show that in this region of the parameter $R$ the effective long-range interaction between kink and antikink takes place.