  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.
