  We study the short pulse dynamics in the deterministic and stochastic
environment in this thesis. The integrable short pulse equation is a modelling
equation for ultra-short pulse propagation in the infrared range in the optical
fibers. We investigate the numerical proof for the exact solitary solution of
the short pulse equation. Moreover, we demonstrate that the short pulse
solitons approximate the solution of the Maxwell equation numerically. Our
numerical experiments prove the particle-like behaviour of the short pulse
solitons. Furthermore, we derive a short pulse equation in the higher order.
  A stochastic counterpart of the short pulse equation is also derived through
the use of the multiple scale expansion method for more realistic situations
where stochastic perturbations in the dispersion are present. We numerically
show that the short pulse solitary waves persist even in the presence of the
randomness. The numerical schemes developed demonstrate that the statistics of
the coarse-graining noise of the short pulse equation over the slow scale, and
the microscopic noise of the nonlinear wave equation over the fast scale, agree
to fairly good accuracy.
