# Embedded solitons in the double sine-Gordon lattice with the next neighbor interactions

## TL;DR

This paper investigates embedded solitons in a discrete double sine-Gordon lattice with next-neighbor interactions, analyzing how these interactions influence soliton existence and potential applications to Josephson junction arrays.

## Contribution

It introduces the effects of next- and second-neighbor interactions on embedded solitons in the double sine-Gordon lattice, expanding understanding of their existence conditions.

## Key findings

- ES existence depends on the sign of interactions
- Narrower linear spectrum widens ES existence range
- Application potential in Josephson junction arrays

## Abstract

Topological solitons can propagate without radiation in discrete media. These solutions are known as embedded solitons (ES). They come as isolated solutions and exist despite their resonance with the linear spectrum of the respective lattices. In this paper the properties of embedded solitons in the discrete double sine-Gordon equation with the next-neighbor and second-neighbor interactions are investigated. Depending on the sign of these interactions they can be either destructive or favorable for the ES creation. The ES existence area depends on the width of the linear spectrum: narrowing of the spectrum widens the ES existence range and vice versa. The application to the Josephson junction arrays is discussed.