Using renormalization group techniques, we derive an extended shortpulse equation as approximation to a nonlinear wave equation. We investigate the new equation numerically and show that the new equation captures efficiently higherorder effects on pulse propagation in cubic nonlinear media. We illustrate our findings using one-and two-soliton solutions of the first-order short-pulse equation as initial conditions in the nonlinear wave equation.
We study the propagation of ultra-short short solitons in a cubic nonlinear
medium modeled by nonlinear Maxwell's equations with stochastic variations of
media. We consider three cases: variations of (a) the dispersion, (b) the phase
velocity, (c) the nonlinear coefficient. Using a modified multi-scale expansion
for stochastic systems, we derive new stochastic generalizations of the short
pulse equation that approximate the solutions of stochastic nonlinear Maxwell's
equations. Numerical simulations show that soliton solutions of the short pulse
equation propagate stably in stochastic nonlinear Maxwell's equations and that
the generalized stochastic short pulse equations approximate the solutions to
the stochastic Maxwell's equations over the distances under consideration. This
holds for both a pathwise comparison of the stochastic equations as well as for
a comparison of the resulting probability densities
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.