  The low-temperature orthorhombic (LTO) phase transition in
La$_{2-x}$Sr$_x$CuO$_4$ can be interpreted as a dynamic Jahn-Teller effect, in
which the degenerate electronic states are associated with the large densities
of states at the two van Hove singularities. The equations describing this
phase are strongly nonlinear. This paper illustrates some consequences of the
nonlinearity, by presenting a rich variety of exact nonlinear wave solutions
for the model.
  Of particular interest are soliton lattice solutions: arrays of domain walls
separating regions of local low-temperature tetragonal (LTT) symmetry. These
arrays have a {\it macroscopic} average symmetry higher than LTT. These
lattices can display either orthorhombic (`orthons') or tetragonal (`tetrons')
symmetry, and can serve as models for a microscopic description of the dynamic
JT LTO and high-temperature tetragonal phases, respectively.
