  The discrete static properties of a class of deformable double-well potential
models are investigated. The Peierls-stress potential of the models is
explicitely given. Numerical analysis of the equation of motion reveal
different soliton wavetrain profiles, most of which are periodic. Soliton
wavetrains are also found analytically in terms of continuum nonlinear periodic
wavefunction solutions then called periodons. The periodon stability in a
lattice phonon bath is discussed. Looking at bifurcation phenomena and routes
to chaos for a representative model of this class, the return map is derived in
terms of a two-dimensional, two-parameter map. This map appears to be area
preserving, possesses three characteristic fixed points with one elliptic, and
displays complex bifurcation diagrams with hopf-like singularities. The routes
to chaos also show complexities all due to the interplay of two control
parameters.
