  The periodic and step-like solutions of the double-Sine-Gordon equation are
investigated, with different initial conditions and for various values of the
potential parameter $\epsilon$. We plot energy and force diagrams, as functions
of the inter-soliton distance for such solutions. This allows us to consider
our system as an interacting many-body system in 1+1 dimension. We therefore
plot state diagrams (pressure vs. average density) for step-like as well as
periodic solutions. Step-like solutions are shown to behave similarly to their
counterparts in the Sine-Gordon system. However, periodic solutions show a
fundamentally different behavior as the parameter $\epsilon$ is increased. We
show that two distinct phases of periodic solutions exist which exhibit
manifestly different behavior. Response functions for these phases are shown to
behave differently, joining at an apparent phase transition point.
