  We study a new family of models of the sine-Gordon type, starting from the
sine-Gordon model, including the double sine-Gordon, the triple one, and so on.
The models appears as deformations of the starting model, with the deformation
controlled by two parameters, one very small, used to control a linear
expansion on it, and the other, which specifies the particular model in the
family of models. We investigate the presence of topological defects, showing
how the solutions can be constructed explicitly from the topological defects of
the sine-Gordon model itself. In particular, we delve into the double
sine-Gordon model in a braneworld scenario with a single extra dimension of
infinite extent, showing that a stable gravity scenario is admissible. Also, we
briefly show that the deformation procedure can be used iteratively, leading to
a diversity of possibilities to construct families of models of the sine-Gordon
type.
