  We study the fully nonlinear dynamical Cosserat micropolar elasticity problem
in space with three dimensionals with various energy functionals dependent on
the microrotation $\overline{R}$ and the deformation gradient tensor $F$ . We
derive a set of coupled nonlinear equations of motion from first principles by
varying the complete energy functional. We obtain a double sine-Gordon equation
and construct soliton solutions. We show how the solutions can determine the
overall deformational behaviour and discuss the relations between wave numbers
and wave velocities thereby identifying parameter values where the waves cannot
propagate.
