  We investigate infinite strings in $(2+1)D$ space-time, which may be
considered as excitations of straight lines on the spatial plane. We also
propose the hamiltonian description of such objects that differs from the
standard hamiltonian description of the string. The hamiltonian variables are
separated into two independent groups: the "internal" and "external" variables.
The first ones are invariant under space-time transformations and are connected
with the second form of the world-sheet. The "external" variables define the
embedding of the world-sheet into space-time. The constructed phase space is
nontrivial because the finite number of constraints entangles the variables
from these groups. First group of the variables constitute the coefficients for
the pair of first-order spectral problems; the solution of these problems is
necessary for the reconstruction of the string world-sheet. We consider the
excitations, which correspond to "N- soliton" solution of the spectral problem,
and demonstrate that the reconstructed string has cuspidal points. World lines
of such points form braids of various topologies.
