  We develop a Riemann-Hilbert approach to the inverse scattering transform
method for the short pulse (SP) equation $u_{xt}=u+\frac{1}{6}(u^3)_{xx}$ with
zero boundary conditions (as $|x|\to\infty$). This approach is directly applied
to the Lax pair for the SP equation. It allows us to give a parametric
representation of the solution to the Cauchy problem. This representation is
then used for studying the long-time behavior of the solution as well as for
retrieving the soliton solutions. Finally, the analysis of the long-time
behavior allows us to formulate, in spectral terms, a sufficient condition for
the wave breaking.
