(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Amiranashvili, Shalva; Radziunas, Mindaugas; Bandelow, Uwe; C̆iegis, Raimondas
We consider a one-dimensional first-order nonlinear wave equation (the
so-called forward Maxwell equation, FME) that applies to a few-cycle optical
pulse propagating along a preferred direction in a nonlinear medium, e.g.,
ultrashort pulses in nonlinear fibers. The model is a good approximation to
the standard second-order wave equation under assumption of weak
nonlinearity. We compare FME to the commonly accepted generalized nonlinear
Schrödinger equation, which quantifies the envelope of a quickly oscillating
wave field based on the slowly varying envelope approximation. In our
numerical example, we demonstrate that FME, in contrast to the envelope
model, reveals new spectral lines when applied to few-cycle pulses. We
analyze and compare pseudo-spectral numerical schemes employing symmetric
splitting for both models. Finally, we adopt these schemes to a parallel
computation and discuss scalability of the parallelization.
