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We study the short pulse dynamics in the deterministic and stochasticenvironment in this thesis. The integrable short pulse equation is a modellingequation for ultra-short pulse propagation in the infrared range in the opticalfibers. We investigate the numerical proof for the exact solitary solution ofthe short pulse equation. Moreover, we demonstrate that the short pulsesolitons approximate the solution of the Maxwell equation numerically. Ournumerical experiments prove the particle-like behaviour of the short pulsesolitons. Furthermore, we derive a short pulse equation in the higher order.  A stochastic counterpart of the short pulse equation is also derived throughthe use of the multiple scale expansion method for more realistic situationswhere stochastic perturbations in the dispersion are present. We numericallyshow that the short pulse solitary waves persist even in the presence of therandomness. The numerical schemes developed demonstrate that the statistics ofthe coarse-graining noise of the short pulse equation over the slow scale, andthe microscopic noise of the nonlinear wave equation over the fast scale, agreeto fairly good accuracy.

Modeling of Ultra-Short Soliton Propagation in Deterministic and Stochastic Nonlinear Cubic Media