TY - JOUR
T1 - A Time-Splitting Spectral Method for Three-Wave Interactions in Media with Competing Quadratic and Cubic Nonlinearities
AU - W. Bao & C. Zheng
JO - Communications in Computational Physics
VL - 1
SP - 123
EP - 140
PY - 2007
DA - 2007/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7899.html
KW - 
AB - <p style="text-align: justify;">This paper introduces an extension of the time-splitting spectral (TSSP) method
for solving a general model of three-wave optical interactions, which typically
arises from nonlinear optics, when the transmission media has competing quadratic
and cubic nonlinearities. The key idea is to formulate the terms related to quadratic
and cubic nonlinearities into a Hermitian matrix in a proper way, which allows us to
develop an explicit and unconditionally stable numerical method for the problem. Furthermore,
the method is spectral accurate in transverse coordinates and second-order
accurate in propagation direction, is time reversible and time transverse invariant, and
conserves the total wave energy (or power or the norm of the solutions) in discretized
level. Numerical examples are presented to demonstrate the efficiency and high resolution
of the method. Finally the method is applied to study dynamics and interactions
between three-wave solitons and continuous waves in media with competing
quadratic and cubic nonlinearities in one dimension (1D) and 2D.</p>